numerical integration __ integral limits being variables

Hello, I want to numerically integrate functions whose upper limits x, lower limits 0. Say;

int_0^x f(x) dx

Which method should I use. trapz, simpson, or omething else and which command ?

I mean can you send a simple example of doing this please? Thanks

Answer 1

[Roger Stafford]

There are a number of ways you can proceed. One way is to use 'int' with a variable upper limit. See:

   http://www.mathworks.com/help/symbolic/int.html

If that does not succeed (which often happens) you can do numerical integration using the 'cumtrapz' function which also allows you to have a variable, though discrete, upper limit. See

   http://www.mathworks.com/help/matlab/ref/cumtrapz.html

Finally, there are several functions in the File Exchange which are numerical but have higher precision. I wrote one of these. It is located at:

   http://www.mathworks.com/matlabcentral/fileexchange/19152-cumulative-cubic-integration

Answer 2

[Star Strider]

If you are numerically integrating functions, use integral (or quad and its friends if you don’t have integral). You will obviously have to define what value ‘x’ is to do a numerical integration.

If you want to do a symbolic integration (and your function is integrable), use the Symbolic Math Toolbox int function.

[Meva]

I have used

u13B = cumtrapz(x, function of x)

Is it true to use ? Many thanks

[Star Strider]

You can use cumtrapz with data returned by your function, but not with your function itself. If you want to use a function, you have to use integral or quad, as I wrote before.

[Meva]

what do you mean by that Can you explain more please?

I have used like:

x=linspace(0,1,0.01)
cumtrapz(x, 4*(x-0.5))

Can't I use it? It is supposed to be

int_0^x  4*(x-0.5) dx