Double integral with cos(x^n) term

[BilalX]

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

Homework Statement

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

Homework Equations

N/A

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.

 

[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.

 

[rootX]

your limits should change too!
I think you did not change the limits

 

[BilalX]

Great, thanks, I went back and realized I'd made a stupid mistake and somehow used a square root instead of the cubic root when changing the limits.