Integrate sin(a*x^2) from -a to a

  • Thread starter maze
  • Start date
  • #1
655
3
Hey all, this should be a simple integral, but I cant seem to solve it. I tried some simple u-subs and integration by parts, but to no avail. Also, maple throws out some Fresnel function.

[tex]\int_{-a}^{a} x^{2} cos\left( a x^{2} \right) dx[/tex]
 

Answers and Replies

  • #2
Defennder
Homework Helper
2,591
5
Well, that should tell you it doesn't have an anti-derivative expressible in terms of elementary functions.
 
  • #3
655
3
I was hoping that perhaps it had a nice representation due to the limits of integration.

edit: I also don't particularly trust maple, as there have been times in the past where it couldn't do integrals that I could. (or perhaps I am using it wrong)
 
Last edited:
  • #4
1,752
1
I was hoping that perhaps it had a nice representation due to the limits of integration.
From the looks of it, it's symmetric, so you can change the limits of integration from 0 to a and multiplying your integral by 2. Idk if that helps at all or not :p
 
  • #5
655
3
This is not a homework question. I am not a student. Please move the question back to the appropriate forum.
 
  • #6
Defennder
Homework Helper
2,591
5
Well if it were an odd function, we would be able to conclude that the answer is 0 without having to work out the anti-derivative. But this is an even function.

By the way, if you want your thread to be moved back you should request a PF mentor by private messaging to do so.
 
  • #7
378
2
>> syms x;
>> f = x^2*cos(x^2);
>> int (f,x)

ans =

1/2*sin(x^2)*x-1/4*2^(1/2)*pi^(1/2)*FresnelS(2^(1/2)/pi^(1/2)*x)


>> int(f,x,-1,1)

ans =

sin(1)-1/2*2^(1/2)*pi^(1/2)*FresnelS(2^(1/2)/pi^(1/2))

Matlab did same ><
I wanted to prove that Matlab is better

"edit: I also don't particularly trust maple, as there have been times in the past where it couldn't do integrals that I could. (or perhaps I am using it wrong)"
sometimes, you need to put the function in integrable form ... (computer's dun think)
 

Related Threads on Integrate sin(a*x^2) from -a to a

  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
8
Views
27K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
23
Views
338K
Replies
2
Views
530
  • Last Post
Replies
4
Views
9K
  • Last Post
Replies
3
Views
3K
Top