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Triple integral and Change of Variables

  1. Nov 24, 2013 #1
    1. The problem statement, all variables and given/known data
    The solid region W is bounded by the ellipsoid x^2/3 + y^2/5 + z^2/7 = 1. Find the triple integral ∫∫∫cos((35x^2 + 21y^2 + 15z^2)^(3/2))dV.


    2. Relevant equations

    Domain: x^2/3 + y^2/5 + z^2/7 = 1

    Integral: ∫∫∫cos((35x^2 + 21y^2 + 15z^2)^(3/2))dV

    3. The attempt at a solution

    I converted the integral to spherical but after that, I do not know where to go. I cannot get rid of the cosine and the whole equation just seems extremely complex.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 24, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    How did you do that? If done in a clever way, I think the problem gets a lot simpler.

    Your domain should have ##\leq 1##.
     
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