Integrate y=x*sin(a*​x^4).*exp(​x^2./2)

How can I integrate this function it gives me the same integrate as the answer integrating from [1 to 5] y=x*sin(a*x^4).*exp(x^2./2)

[darova]

What have your tried? Any ideas?

Answer 1

[Thiago Henrique Gomes Lobato]

Matlab can't find the close integral form for all functions (some may even not have one). If you are interested only in the value of the definite integral, you can evaluate it both with the symbolic toolbox with a given precision or numerically by specifiying a value for a:

a = 2; % Specify a Value 

% Symbolic
syms y x
y=x*sin(a*x^4).*exp(x^2./2);
ySymbolic = vpa(int(y,x,[1 5]),8)

% Numeric
f = @(t)t.*sin(a*t.^4).*exp(t.^2./2);
yNumeric = integral(f,1,5)

Difference = ySymbolic-yNumeric

yNumeric =

  -1.2607e+03
  
ySymbolic =
 
-1260.7316

Difference =
 
0.00000000009231371222995221614837646484375