# Double integration with cos x^2

1. Nov 4, 2007

### raynoodles

ok so I have the problem ycos(x^2)dxdy with parameters dx=y^2 to 1 and dx=0 to 1
the first problem I have is integrating cos with respect to x^2. is it a double angle identity? the second is how do I go further if Y^2 gets added into the mix later?
The attempts I have made have made me even more confused than before. I looked up how I could integrate cos x^2 and could not find a clear answer.
Help is appreciated.

2. Nov 4, 2007

### Galileo

Did you copy the limits of integration correctly?
Should it be x going from y^2 to 1 and then y going from 0 to 1?

3. Nov 4, 2007

### Antineutron

What is the identity of cosx^2? if you don't know then look it up in your book.

4. Nov 5, 2007

### Gib Z

It can't be expressed in terms of elementary functions, look up the Cosine Fresnel integral for the solution.

5. Nov 5, 2007

### Galileo

Not so fast.
Try reparametrizing your region of integration. If you first integrate wrt y, then wrt x you may find a solution. (Hint: You will).

6. Nov 5, 2007

### Gib Z

O sorry I should have read the whole question, Mainly just read post 3 and replied to that.