Triple integral and Change of Variables

[frogger832]

Homework Statement

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.

Homework Equations

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

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

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.

 

[mfb]

I converted the integral to spherical

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

Your domain should have $\leq 1$.