# Double integral with cos(x^n) term

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

1. Homework Statement

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. Homework 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.