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

Hi guys, I need help setting up an integral.

Problem: Compute the integral f(x,y,z)=xyz over the solid region bounded below by plane z=-x, above by z=x, and otherwise b the parabolic cylinder x=2-y^2

This is not a surface integral, is it? Because the problems assigned to me before and after this question dealt with surface integrals.

**2. Relevant equations**

I'm going to assume it's not a surface integral. I can see clearly that my bounds for z will be between -x and x. I will hazard a guess that my y bounds might be sqrt(2-x) and -sqrt(2-x).

How can I figure out my x bounds algebraically. I have terrible 3-d intuition. I can draw a 3-d graph pretty well but it's hard for me to visualize it.

**3. The attempt at a solution**

I'm great at solving integrals once they're set up. Just need help with my bounds.

Thanks