Triple integral problem

1. Mar 2, 2009

halcyone

1. The problem statement, all variables and given/known data

A triple integral, with the bounds, from outer to inner:
integrate from -1 to 1 with respect to x
integrate from 0 to 1-x^2 with respect to y
integrate from 0 sqrt (y) with respect to z
on the function x^2*y^2*z^2

2. Relevant equations
none

3. The attempt at a solution
I know what kind of a region it is. The region intersects at x^2+z^2=1. However, my attempts at solving this integral lead to a messy, impossible looking integral, and I am fairly sure that this integral requires no more than integration by parts. I've tried changing the bounds, such as letting D=half-circle in xz plane, and let the bounds on y be from z^2 to 0, but they lead to similar problems. What else can I do?....

2. Mar 2, 2009

Feldoh

Try a transformation from rectangular to something else...