{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-16T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":50489,"title":"Find the area between curves (P1)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none 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width=\"62.5\" height=\"18\" style=\"width: 62.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e)          \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [3.5773, 6.1773, 5.5773, 11.2970]\r\n    assert(isempty(strfind(filetext, num2str(ii))), ... \r\n    'Do NOT use provided answers in your solution')\r\nend\r\n%%\r\na = 1; \r\nb = 1;\r\n\r\ny_correct = 3.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 3; \r\nb = 0.3; \r\n\r\ny_correct = 6.1773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = -1;\r\nb = 4;\r\n\r\ny_correct = 5.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = exp(1);\r\n\r\ny_correct = 11.2970;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T12:36:27.000Z","updated_at":"2026-01-23T10:01:56.000Z","published_at":"2021-02-19T12:40:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area between the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^2\\\\, \\\\mathrm{e}^{- x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = a\\\\, x + b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e over the interval [0 2] for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                                                                                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e     \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                        plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=b=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e)          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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50499,"title":"Find the area between curves (P2)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 612.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 306.25px; transform-origin: 407px 306.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Area between curves - Problem 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 32.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 16.25px; text-align: left; transform-origin: 384px 16.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Find the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63.5\" height=\"20\" style=\"width: 63.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIgAAABACAYAAADBAT+LAAAJN0lEQVR4Xu2cB8w1RRWGH5AiCiGiqEgRDcagUWOMCCIgJChgAKMUpcWOgvQgVZCmoBSli6AgoJBQFCSAYFSkWegxakAJYkN6kaK0POQMGTd799u97b/3uzPJl///vrs7O+fMO+e85525uxClFQ80eGCh4p3igSYPFIAUfDR6oACkAKQApGCgfw+UCNK/72bizgKQmZjmnkYuC2wPPAccVndVAchsAuTlwLbANsCawAHAIQUgswmGOqsXjajxHuDqApACjF4eMHoUgBR89PRAAUgBR6MHCkAKQApACgb690CJIP37bibuLACZiWnu38gCkP59NxN3FoDMxDT3b2QBSP++m4k71wZ+WZTUmZjrTkYuFXswnwI2B34NHAFcC9yT91Q26zr5dfYuLgCZvTnvZHEBSCd3zd7FBSCzN+edLC4A6eSuqb/4UmCDFlZsCFzmdQUgLbw1jy4pAJlHkzkRppQIMhHTMLmDKACZ3LmZiJEVgEzENEzuIApAJnduJmJk4wTIEsBawFXAkwNavzCwLnAT8MCAfZXbGzwwLoD4Da79gZOBPwxpRpYH9gC+Bdw1pD5LNxUPjAMgrwG+Ahw7RHAkM+x7rwKS0eF61AAxrbiNfD3ww/g217Ct8dDLx4C9gf8Mu/NZ72/UAHHi3h+pYFST9xLgS8DjEaX8InJp9R7QV2sAHhTy378C+wFK6/sAiwFbAzek20cJkOWA7wBfD2I6ykl7A3BSAPH3o3zQPOl7O+AM4BPAMsAdwKuBU4HPAKeNAyCfBtYBdgQeHbFjXRl+O/1p4CDgmRE/b5q7NygYNbYArgB+BfwY2BX4AiB4pAQvtFFFkKUDjVcC3x6TN9cPkHwcuHNMz5zGx6S52Qw4FPhqGHEMYNT/LPDvUQPkXcD5QR5fROOIvbkKcA5wMHDRiJ81zd2/HTgP+BfwSeDPwOuBHwC/AA6MSDzSCOJbawxVW41Ro0grQw5imilktR7GktCzgC+GLmU6TqfbPwJcmN/WJsWsFJHgA0FmrEbeAfwofp4IjvHf6DjxgTcF4Xm4xXJ7BfDeOGFt1aPSmrPp10ZksCqSQO0L+Ny8ycAPB141Jt7TwqzOl/jmn03DD7cD/n4rIPi13UM8X844loryisBGwCZxUt3ouRPwYFAIqxX98tYAxbvj0JD92bcY2C0W9JbhvxuTf5sA4sPt5DjgOmBn4C9Zh0dl5r8PuCZ+f1kIVyLTB1cnss5rgumhcMQpIaN/LZzhhPss+5FnmLI+BzxS05HOczUYue7tMD2vBM4GPtjhnrpL5Vttba4uVLcOnMjfhrDo+NPkJV8Lnjx9Lg68EfgH4ByoNfmVBhezBNQiwfG4eD1JJt/wb/fHfLpNkSLv/4CLgUWiHwl/I0l1MGcCjwVQ3ENJLYUpc5b/d4CpJWeLwhztbXyfoo81+SXADsGuZdl+wWeu5n2uAn/+NNfFNWNeEABxIQroE8Pfajq5ZpR87XdWmlL26wLkRmAjrBHerQgrlvRdF7mhIFC8PD4ikWKmUoR9e9/380XdK4KIwhPiRWenR2jKBy3HcF/llprJSAAxotS+GG2OiTNUCojbon+BaX3ehlPozD37AEgHLA31Uv1v1aUvtVMNQvKYNyPA0eGDXUIQrBtESrFe7+IyarjFYRrpu/UCSKoIRNzugCVQavlALGOr4XxQgCSWbdoRzebTunRSZ/S0AURbrbxWACw7f1ox6qWRXo2k1Xmosz8tXD8zDbddWD0B1AYgvirR/JyaqqW5zjfkGQ5Fdy5MDZJifIaE1dT2oZZOyY0zpZka5U6qg5PcDO0uPCe110JI5efbQg5PPK+XXasHyKQFG+eSeb+O6AUQ2bM5Sin285nYJYFxU8zUYRrQuP/7LifQD0nNxy/xOjLSWlfSJ0DcvDOSSMQmua0WPEFx6qPABTWDbeJ6dbZJWI1IVirVhd2XL5qqmDdHSSkarZn/Hg9VfTs38lvdYZ1+ytx88Ikcy4PqSHAvQ9OK9PlNubru/nFXMUnudqH5xek69de9Efey5GRGGhdmkhLqbHBh+bZkiaktVYEDbTs0AcTPTCMe9PkN8BRwd2j3f5uDNIp882ZXoWzVMEyxRgOXbBla89RkGPbeLm3cAMmLANNpdb9K3ysrfDOMyKN4nV2J7KolWR5LTtVMfJvyfV0cUb22F0Bydm30MEd2aYl8qevPlTdTv6Y1dQBlYNVQHWftnpxjelMrcMXVkdb0TEntz7oMdgFcmwOyLo2qVViymzIUCdU1ftdgvwvLg1P+WGD4BSmrIYmvVYwn+hTKrJSe7WJvL4DkRFHhRunacN/2TEfiMJaqhse6EtX6X5FG1VSRxtDo4CW9NsOvTtKBfmbq0bFyo7r+jFpyJiX+f3ZxwgK4No8g+Up3PlwEppyfxCLRh+md6qYLOYav0tbH7pLrE49dKmi6GHM9xPvUQ/Sley2CrFPrBRDzuGWVAkreHLT6yM8j5TQ9TF3fAbrtr+xbbVYpVkOCw91XI0MuEnm/G346QSe6IgRMHUgTIG+ekkND+l3NQ9XY5lkWtQsjpp/5cn0P8bhn4hleD/Bom0BwYTnh+kox0EUlL0wn9uQizpspSp1KWuBnfZ3oqwOIf1O/l0N4qMSQJaI9kZ6a5EnS1HSi3Cik4Q7MiqfaJMGC7Z3x7zcq50YMi/7N8Pq90AN6Pc+KwCin0yXT09CcSCOewpa2mha/my0+qzH3nSSmSuSmXuVv58e3AgkCU618wyiRpw7nz8htRZnf29kvVYA4aCsA62kPj6QSVtS+JVRKQ7jNXG+4b2rmUiOIfdZFkc4DrrnB6sW0pBRv+C1tiB6oAsQ87qr9cFQu1UcJIEObZy7aaBQpVdlPVVAbhhmJTBuFrLastEobogdygCRZ19DWtNmVXp3Yts52hXucTY4hd2mzp9LWRLcC5CpWP6M+1th2TPPquhwgSeCyrJUg9SpPTRkqlkabtiWsIDElWXJdPiSQCA5FJFXXAo4RwbKaYhIx+mOINznhk4cIHI+kuWIVs7pEA+9fOY7av3DWYIAmmNUIPLZf0soAjpzr1roqJp0gWy9KS8ss2bB/9+CQjPnFQ61zPaB8Pt0eaHPkcLotLKMfyAMFIAO5b/7fXAAy/+d4IAsLQAZy3/y/+XmCvwRfEztUNwAAAABJRU5ErkJggg==\" width=\"68\" height=\"32\" style=\"width: 68px; height: 32px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; 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src=\"data:image/png;base64,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\" 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src=\"data:image/png;base64,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\" width=\"29.5\" height=\"19\" style=\"width: 29.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJkAAAAkCAYAAACaCJgRAAAFsklEQVR4Xu2bdag1VRTFf5+J2A0qFooKJoKNhY0JdqBgKzYodgdiFyaKrdhiYHcH6l+C2BhY2IjJT/bAvHkz787c981372XOwONx7ztzzpw16+yz9trnTSFdCYGWEZjScv+p+4QAiWSJBK0jkEjWOsRpgESyxIHWEUgkax3iNEAiWeJA6wgkkrUOcRqgyyRbFDgEeAu4LVGhJwLTAasDewMbAYsBzwJ3ATcBP1b10EWSSa6DgH2BeYDdgVt6QtztBrMARwFHAx8A3wTJlglYHgIOAD4vg6lLJJsL2AdwRS4SUUxMEskmXkBy5NCIYicAHwH/Bo6bA5cH4U4HTgX+LnbXJZLNAPwTP8sCdwIrJJL1DNFGq/2AU4CfC62nByTXsYDRbA/ghy6TLD93gbsDWCmRrCfJdgbeBt6vaLkbcHNoM3eKcdqsS5Eskawnn/pqsD9wZWi2C2MrHdNRIlnSZH0xK26aA7gUmBOQbF/3K/wlohrGULhQhM2Fgfviu6WBXYF3J/O00/jeNrfLmQDxWRlYFVgjxPG9wMzAlsCBwGrArcDxwHfTeP5TYzgTKN/7dsCRwCf9Whim+KatAnMM8EgI5yXCW9I30Scp3YtLBs2/3MlM9KQQnP320SbJlgc2BvYMzfcqsEtoFUXy/MCMwLbx8NsAD9ScSKZ/ajavbLYO8OIkOnEOWhpaQR8DZwP3AH80jWSuRtNTV6SAabxl17zhLW0aLHYvrnN1gWTioK8kJm4hVwEnAicDr0T0WhN4IQDbBHi8DnjAoEm2HHBwLBoDUP66IgLSr8W5VGmyBQMcV5lpqWal3kh26fYa6tcC1gOeqwnSsDRrM5I5R2WFmK0P7AWIp0allQVx3Am4HciinN7TKF1KAk1tt8vDwtT2+d3RrqtDMv0kTbXjgBvDtPypcKM64zHgvRiocj8eUuTaJtnaIS0+jN9iqpHpduLCNqr5Y5Q7Avh9SHGq81jKg2vDrLW8ZKQb46eVRbJ1Y5XNBmwfZCoOJjAXjDBIbZMsw0ewn4qSy1cBopmYL0VsS1d+nTc7RG3kkPO4GnipLOgUSWb2c26UEcyGLIYWHdwFgGuArQM8V+OoXW2SbPbQssqML8PslWjZtWIkS36WaKOUlVe952xOv4UUGGPcFkmWB9/socxcy8SnAG4FvNmAYV0Q/vk5XhJiOJ919XTIJ8Bz0MK/6tGyOas7x5WWiiQz9VZreZVlPYtHCUHN8UxkO18kko1BwAh/f+gSC8h5q0DBfE7oMDPOM8sc8hEkmX7ggyEDxhXJiyTLr5SilzJreFNaGhsApqxGOzMp09k3GpBt0E2bbJeajuqoP4Ffejx4vmBcJjfyWaeL+InIQD0+89mgQelzfDmkBvWkhtv/OB5MFMnyR2DUGRqJdmAU8+yQLq8nGQ4HzqsqKfT54G3fVpdkZoUuJKOPIl4MlBB/VTzgfHGAb7OKWl6WdZqVu6CXDMPW0kxVn21j0at/nQQx0CfVgilWJzzJcn0kgplFM6bPIsk0YE1DjVTvABeHwy/hzg+SWXHXhNXpd+V6zKOqQt9rAoP6u9vYwzF4lfb0z3nT2c9iosdVNd9s2zAzL26V3p/tFPZzNzB3GLXjDMxBAVMyru/3rPj+deAi4Mn4vEVkkzr+T1dt/WUWhnXK0wBXo2HccoF+2afhZDugWack0+sZlTBv5rwhoMG8Q85A/B64IRz454Fvc0AbydwGrC9mDvdEJZnsRMKjIYDzfdntUjGWhyYd04VbPKM1RPz6/1Gct7vVjkB2EtbKxWuAkuDlqnJSNpGunsLo50Var7sMsG46apG7n/lOtXsSyepDaRTUqD5jiPVT/dlMw5aJZPXAtjCsdnPbLD0zVa+bbrZKJOv93leJ1FzB63/ppKshAolkDQFLzZsjkEjWHLN0R0MEEskaApaaN0cgkaw5ZumOhgj8B8RbNDQv76XCAAAAAElFTkSuQmCC\" width=\"76.5\" height=\"18\" style=\"width: 76.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, n)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.5, 0.6667, 1.3606, 2.7754, 22.3242]\r\n    assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\n\r\n%%\r\na = 1; \r\nn = 3;\r\n\r\ny_correct = 0.5;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1; \r\nn = 5; \r\n\r\ny_correct = 0.6667;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nn = 2.5; \r\n\r\ny_correct = 1.3606;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nn = 3.1;\r\n\r\ny_correct = 2.7754;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(3);\r\nn = 12;\r\n\r\ny_correct = 22.3242;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T15:56:21.000Z","updated_at":"2025-08-25T11:22:08.000Z","published_at":"2021-02-19T15:59:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Area between curves - Problem 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Find the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = ax^{\\\\frac{1}{n}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e for different \\\"n\\\"  and \\\"a\\\" coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                       Plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and  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the area between curves (P4)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 601px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 300.5px; transform-origin: 407px 300.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" 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style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"126\" height=\"18\" style=\"width: 126px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b, c)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [6.5065, 6.3475, 0.1134, 9.4710, 4.0104]\r\n    assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\nassert(isempty(strfind(filetext, 'if')),'if: Forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch: Forbidden')\r\n%%\r\na = 1;\r\nb = 1;\r\nc = -2;\r\n\r\ny_correct = 6.5065;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1;\r\nb = 2.5;\r\nc = -5; \r\n\r\ny_correct = 6.3475;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 0;\r\nb = 4.8;\r\nc = -0.5; \r\n\r\ny_correct = 0.1134;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = pi;\r\nc = -pi;\r\n\r\ny_correct = 9.4710;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2;\r\nb = 70;\r\nc = -6;\r\n\r\ny_correct = 4.0104;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-20T22:13:12.000Z","updated_at":"2026-01-18T15:37:37.000Z","published_at":"2021-02-20T22:13:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = y^4 - a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = bx + c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43648,"title":"Arc length of points interpolation","description":"Given a n by m matrix representing m vectors in n dimensions. Calculate the \u003chttps://en.wikipedia.org/wiki/Arc_length arc length\u003e of the closed loop curve going though these points in the order that they are given. The parametric curve, |c(t)| , between points |p(k)| and |p(k+1)| is defined as,\r\n\r\n|c(t) = p(k-1) * (-t/2+t^2-t^3/2) + p(k) * (1-5/2*t^2+3/2*t^3) + p(k+1) * (t/2+2*t^2-3/2*t^3) + p(k+2) * (-t^2/2+t^3/2)|,\r\n\r\nwhere |t| goes from 0 to 1. These interpolation polynomials can also be found using the constraints |c(0)=p(k)|, |c(1)=p(k+1)|, |c'(0)=(p(k+1)-p(k-1))/2| and |c'(1)=(p(k+2)-p(k))/2|.\r\n\r\nFor example for the points\r\n\r\n  points = [[1; 0] [0; 1] [-1; 0] [0; -1]];\r\n\r\nwould yield to following curve: \r\n\r\n\u003c\u003chttp://i.imgur.com/CIb8jFU.png\u003e\u003e","description_html":"\u003cp\u003eGiven a n by m matrix representing m vectors in n dimensions. Calculate the \u003ca href = \"https://en.wikipedia.org/wiki/Arc_length\"\u003earc length\u003c/a\u003e of the closed loop curve going though these points in the order that they are given. The parametric curve, \u003ctt\u003ec(t)\u003c/tt\u003e , between points \u003ctt\u003ep(k)\u003c/tt\u003e and \u003ctt\u003ep(k+1)\u003c/tt\u003e is defined as,\u003c/p\u003e\u003cp\u003e\u003ctt\u003ec(t) = p(k-1) * (-t/2+t^2-t^3/2) + p(k) * (1-5/2*t^2+3/2*t^3) + p(k+1) * (t/2+2*t^2-3/2*t^3) + p(k+2) * (-t^2/2+t^3/2)\u003c/tt\u003e,\u003c/p\u003e\u003cp\u003ewhere \u003ctt\u003et\u003c/tt\u003e goes from 0 to 1. These interpolation polynomials can also be found using the constraints \u003ctt\u003ec(0)=p(k)\u003c/tt\u003e, \u003ctt\u003ec(1)=p(k+1)\u003c/tt\u003e, \u003ctt\u003ec'(0)=(p(k+1)-p(k-1))/2\u003c/tt\u003e and \u003ctt\u003ec'(1)=(p(k+2)-p(k))/2\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eFor example for the points\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003epoints = [[1; 0] [0; 1] [-1; 0] [0; -1]];\r\n\u003c/pre\u003e\u003cp\u003ewould yield to following curve:\u003c/p\u003e\u003cimg src = \"http://i.imgur.com/CIb8jFU.png\"\u003e","function_template":"function dist = arcLength(points)\r\n    dist = 1;\r\nend","test_suite":"%%\r\npoints = [[1; 0] [0; 1] [-1; 0] [0; -1]];\r\ndist_correct = 5.945066529883204;\r\nassert(abs(arcLength(points) - dist_correct) \u003c 1e-6)\r\n\r\n%%\r\npoints = eye(2);\r\ndist_correct = 2 * sqrt(2);\r\nassert(abs(arcLength(points) - dist_correct) \u003c 1e-6)\r\n\r\n%%\r\npoints = [cos(2*pi/500*(1:500)); sin(2*pi/500*(1:500))];\r\ndist_correct = 6.283185305221142;\r\nassert(abs(arcLength(points) - dist_correct) \u003c 1e-6)\r\n\r\n%%\r\npoints = [[0 0 0]' [1 0 0]' [1 0 1]' [0 0 1]' [0 1 1]' [1 1 1]' [1 1 0]' [0 1 0]'];\r\ndist_correct = 8.367321074314315;\r\nassert(abs(arcLength(points) - dist_correct) \u003c 1e-6)\r\n\r\n%%\r\npoints = [6 -8 -7 -7 3 5;8 -4 9 -1 -9 5;-7 1 9 8 7 -2;8 9 0 6 8 3;3 9 6 9 3 -6];\r\ndist_correct = 101.32625280165301;\r\nassert(abs(arcLength(points) - dist_correct) \u003c 1e-6)\r\n\r\n%%\r\nw = 0.887321243287836;\r\npoints = [-w  0  w  1 1 1 w 0 -w -1 -1 -1; -1 -1 -1 -w 0 w 1 1  1  w  0 -w];\r\ndist_correct = 8;\r\nassert(abs(arcLength(points) - dist_correct) \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":40782,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2016-12-14T19:45:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-30T02:02:55.000Z","updated_at":"2016-12-14T19:45:19.000Z","published_at":"2016-10-30T02:03:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a n by m matrix representing m vectors in n dimensions. Calculate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Arc_length\\\"\u003e\u003cw:r\u003e\u003cw:t\u003earc length\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of the closed loop curve going though these points in the order that they are given. The parametric curve,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec(t)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e , between points\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(k)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(k+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec(t) = p(k-1) * (-t/2+t^2-t^3/2) + p(k) * (1-5/2*t^2+3/2*t^3) + p(k+1) * (t/2+2*t^2-3/2*t^3) + p(k+2) * (-t^2/2+t^3/2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e goes from 0 to 1. These interpolation polynomials can also be found using the constraints\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec(0)=p(k)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec(1)=p(k+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec'(0)=(p(k+1)-p(k-1))/2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec'(1)=(p(k+2)-p(k))/2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for the points\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[points = [[1; 0] [0; 1] [-1; 0] [0; -1]];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewould yield to following curve:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 12.25px; text-align: left; transform-origin: 384px 12.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area between the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89\" height=\"24\" style=\"width: 89px; height: 24px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89.5\" height=\"19\" style=\"width: 89.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e over the interval [0 2] for different \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e coefficients:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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width=\"62.5\" height=\"18\" style=\"width: 62.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e)          \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [3.5773, 6.1773, 5.5773, 11.2970]\r\n    assert(isempty(strfind(filetext, num2str(ii))), ... \r\n    'Do NOT use provided answers in your solution')\r\nend\r\n%%\r\na = 1; \r\nb = 1;\r\n\r\ny_correct = 3.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 3; \r\nb = 0.3; \r\n\r\ny_correct = 6.1773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = -1;\r\nb = 4;\r\n\r\ny_correct = 5.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = exp(1);\r\n\r\ny_correct = 11.2970;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T12:36:27.000Z","updated_at":"2026-01-23T10:01:56.000Z","published_at":"2021-02-19T12:40:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area between the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^2\\\\, \\\\mathrm{e}^{- x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = a\\\\, x + b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e over the interval [0 2] for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                                                                                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e     \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                        plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=b=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e)          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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50499,"title":"Find the area between curves (P2)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 612.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 306.25px; transform-origin: 407px 306.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Area between curves - Problem 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 32.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 16.25px; text-align: left; transform-origin: 384px 16.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Find the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63.5\" height=\"20\" style=\"width: 63.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"68\" height=\"32\" style=\"width: 68px; height: 32px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; 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src=\"data:image/png;base64,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\" 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src=\"data:image/png;base64,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\" width=\"29.5\" height=\"19\" style=\"width: 29.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"76.5\" height=\"18\" style=\"width: 76.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, n)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.5, 0.6667, 1.3606, 2.7754, 22.3242]\r\n    assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\n\r\n%%\r\na = 1; \r\nn = 3;\r\n\r\ny_correct = 0.5;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1; \r\nn = 5; \r\n\r\ny_correct = 0.6667;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nn = 2.5; \r\n\r\ny_correct = 1.3606;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nn = 3.1;\r\n\r\ny_correct = 2.7754;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(3);\r\nn = 12;\r\n\r\ny_correct = 22.3242;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T15:56:21.000Z","updated_at":"2025-08-25T11:22:08.000Z","published_at":"2021-02-19T15:59:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Area between curves - Problem 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Find the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = ax^{\\\\frac{1}{n}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e for different \\\"n\\\"  and \\\"a\\\" coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                       Plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and  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the area between curves (P4)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 601px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 300.5px; transform-origin: 407px 300.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" 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style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"126\" height=\"18\" style=\"width: 126px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b, c)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [6.5065, 6.3475, 0.1134, 9.4710, 4.0104]\r\n    assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\nassert(isempty(strfind(filetext, 'if')),'if: Forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch: Forbidden')\r\n%%\r\na = 1;\r\nb = 1;\r\nc = -2;\r\n\r\ny_correct = 6.5065;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1;\r\nb = 2.5;\r\nc = -5; \r\n\r\ny_correct = 6.3475;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 0;\r\nb = 4.8;\r\nc = -0.5; \r\n\r\ny_correct = 0.1134;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = pi;\r\nc = -pi;\r\n\r\ny_correct = 9.4710;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2;\r\nb = 70;\r\nc = -6;\r\n\r\ny_correct = 4.0104;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-20T22:13:12.000Z","updated_at":"2026-01-18T15:37:37.000Z","published_at":"2021-02-20T22:13:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = y^4 - a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = bx + c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43648,"title":"Arc length of points interpolation","description":"Given a n by m matrix representing m vectors in n dimensions. Calculate the \u003chttps://en.wikipedia.org/wiki/Arc_length arc length\u003e of the closed loop curve going though these points in the order that they are given. The parametric curve, |c(t)| , between points |p(k)| and |p(k+1)| is defined as,\r\n\r\n|c(t) = p(k-1) * (-t/2+t^2-t^3/2) + p(k) * (1-5/2*t^2+3/2*t^3) + p(k+1) * (t/2+2*t^2-3/2*t^3) + p(k+2) * (-t^2/2+t^3/2)|,\r\n\r\nwhere |t| goes from 0 to 1. These interpolation polynomials can also be found using the constraints |c(0)=p(k)|, |c(1)=p(k+1)|, |c'(0)=(p(k+1)-p(k-1))/2| and |c'(1)=(p(k+2)-p(k))/2|.\r\n\r\nFor example for the points\r\n\r\n  points = [[1; 0] [0; 1] [-1; 0] [0; -1]];\r\n\r\nwould yield to following curve: \r\n\r\n\u003c\u003chttp://i.imgur.com/CIb8jFU.png\u003e\u003e","description_html":"\u003cp\u003eGiven a n by m matrix representing m vectors in n dimensions. Calculate the \u003ca href = \"https://en.wikipedia.org/wiki/Arc_length\"\u003earc length\u003c/a\u003e of the closed loop curve going though these points in the order that they are given. The parametric curve, \u003ctt\u003ec(t)\u003c/tt\u003e , between points \u003ctt\u003ep(k)\u003c/tt\u003e and \u003ctt\u003ep(k+1)\u003c/tt\u003e is defined as,\u003c/p\u003e\u003cp\u003e\u003ctt\u003ec(t) = p(k-1) * (-t/2+t^2-t^3/2) + p(k) * (1-5/2*t^2+3/2*t^3) + p(k+1) * (t/2+2*t^2-3/2*t^3) + p(k+2) * (-t^2/2+t^3/2)\u003c/tt\u003e,\u003c/p\u003e\u003cp\u003ewhere \u003ctt\u003et\u003c/tt\u003e goes from 0 to 1. These interpolation polynomials can also be found using the constraints \u003ctt\u003ec(0)=p(k)\u003c/tt\u003e, \u003ctt\u003ec(1)=p(k+1)\u003c/tt\u003e, \u003ctt\u003ec'(0)=(p(k+1)-p(k-1))/2\u003c/tt\u003e and \u003ctt\u003ec'(1)=(p(k+2)-p(k))/2\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eFor example for the points\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003epoints = [[1; 0] [0; 1] [-1; 0] [0; -1]];\r\n\u003c/pre\u003e\u003cp\u003ewould yield to following curve:\u003c/p\u003e\u003cimg src = \"http://i.imgur.com/CIb8jFU.png\"\u003e","function_template":"function dist = arcLength(points)\r\n    dist = 1;\r\nend","test_suite":"%%\r\npoints = [[1; 0] [0; 1] [-1; 0] [0; -1]];\r\ndist_correct = 5.945066529883204;\r\nassert(abs(arcLength(points) - dist_correct) \u003c 1e-6)\r\n\r\n%%\r\npoints = eye(2);\r\ndist_correct = 2 * sqrt(2);\r\nassert(abs(arcLength(points) - dist_correct) \u003c 1e-6)\r\n\r\n%%\r\npoints = [cos(2*pi/500*(1:500)); sin(2*pi/500*(1:500))];\r\ndist_correct = 6.283185305221142;\r\nassert(abs(arcLength(points) - dist_correct) \u003c 1e-6)\r\n\r\n%%\r\npoints = [[0 0 0]' [1 0 0]' [1 0 1]' [0 0 1]' [0 1 1]' [1 1 1]' [1 1 0]' [0 1 0]'];\r\ndist_correct = 8.367321074314315;\r\nassert(abs(arcLength(points) - dist_correct) \u003c 1e-6)\r\n\r\n%%\r\npoints = [6 -8 -7 -7 3 5;8 -4 9 -1 -9 5;-7 1 9 8 7 -2;8 9 0 6 8 3;3 9 6 9 3 -6];\r\ndist_correct = 101.32625280165301;\r\nassert(abs(arcLength(points) - dist_correct) \u003c 1e-6)\r\n\r\n%%\r\nw = 0.887321243287836;\r\npoints = [-w  0  w  1 1 1 w 0 -w -1 -1 -1; -1 -1 -1 -w 0 w 1 1  1  w  0 -w];\r\ndist_correct = 8;\r\nassert(abs(arcLength(points) - dist_correct) \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":40782,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2016-12-14T19:45:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-30T02:02:55.000Z","updated_at":"2016-12-14T19:45:19.000Z","published_at":"2016-10-30T02:03:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a n by m matrix representing m vectors in n dimensions. Calculate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Arc_length\\\"\u003e\u003cw:r\u003e\u003cw:t\u003earc length\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of the closed loop curve going though these points in the order that they are given. The parametric curve,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec(t)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e , between points\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(k)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(k+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec(t) = p(k-1) * (-t/2+t^2-t^3/2) + p(k) * (1-5/2*t^2+3/2*t^3) + p(k+1) * (t/2+2*t^2-3/2*t^3) + p(k+2) * (-t^2/2+t^3/2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e goes from 0 to 1. These interpolation polynomials can also be found using the constraints\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec(0)=p(k)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec(1)=p(k+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec'(0)=(p(k+1)-p(k-1))/2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec'(1)=(p(k+2)-p(k))/2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for the points\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[points = [[1; 0] [0; 1] [-1; 0] [0; -1]];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewould yield to following curve:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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