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Double integral with cos(x^n) term

  1. Apr 6, 2008 #1
    [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):
    \int _{0}^{\frac{1}{8}}\int _{\sqrt[3]{y}}^{\frac{1}{2}}\cos\left(20{\pi}x}} ^{4}\right)dx dy[/tex]

    2. Relevant equations


    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. jcsd
  3. Apr 6, 2008 #2
    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.
  4. Apr 6, 2008 #3
    your limits should change too!
    I think you did not change the limits
  5. Apr 7, 2008 #4
    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.
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