Calculus 3 Triple Integration in Spherical Coords

[Wargy]

Homework Statement

Use spherical coordinates to evaluate the triple integral z dV where Q is the solid that lies between x^2+y^2+z^2=1 and x^2+y^2+z^2=4.

Homework Equations

Not sure what goes here :P

The Attempt at a Solution

I've gotten everything set up, I am having problems with boundaries I think. Currently I am using 0 to 2$$\pi$$ for $$\vartheta$$, 0 to $$\pi$$ for $$\varphi$$ and 1 to 2 for $$\rho$$. When solving, I get zero as my final answer, and since I'm not clear on the conceptual meaning of a triple integral that isn't of a function that equals 1 (volume) I don't know if this answer makes sense.

 

[Dick]

It is zero. It's the integral of z on the volume between two spheres centered on the origin. It's as much positive as negative. The two cancel. But you should be using rho from 1 to 2.

 

[Wargy]

Nevermind, read what you wrote again.
Thanks for the quick reply!

 

[Dick]

Makes a lot of sense.