# Double integral with cos(x^n) term

1. Apr 6, 2008

### BilalX

[SOLVED] Double integral with cos(x^n) term

1. The problem statement, all variables and given/known data

Solve the following integral (without using a series development):
$$\displaystyle \int _{0}^{\frac{1}{8}}\int _{\sqrt[3]{y}}^{\frac{1}{2}}\cos\left(20{\pi}x}} ^{4}\right)dx dy$$

2. Relevant equations

N/A

3. The attempt at a solution

Obviously the cos(x^4) part is what throws me off, I tried switching the order of integration and substituting for various trigonometric identities but it doesn't seem to help much. I'd appreciate any pointers to get me started.

2. Apr 6, 2008

### Mystic998

I think changing the order of integration is the way to go. You'll get an x^3 term in the integral with respect to x. Then it's easy.

3. Apr 6, 2008