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

**1. Homework Statement**

Solve the following integral (without using a series development):

[tex]\displaystyle

\int _{0}^{\frac{1}{8}}\int _{\sqrt[3]{y}}^{\frac{1}{2}}\cos\left(20{\pi}x}} ^{4}\right)dx dy[/tex]

**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.