Evaluating a triple integral Spherical

1. Nov 8, 2013

PsychonautQQ

1. The problem statement, all variables and given/known data
z(x^2+y^2+z^2)^(-3/2) where x^2+y^2+z^2 ≤ 4 and z ≥ 1

3. The attempt at a solution
So spherically this comes down to cos∅sin∅dpdθd∅
p goes from 0 to 2, theta goes from 0 to 2pi, but I don't know how to figure out what ∅ goes from? i'm trying use trig identities but i'm getting the wrong answer, so maybe this don't work since the sphere is curved?

2. Nov 8, 2013

vela

Staff Emeritus
Your limits for $\rho$ aren't correct. For example, consider the part of the z-axis which is inside the solid. It's only the part where 1 ≤ z ≤ 2. This would be inconsistent with $\rho \le 1$, yet your lower limit for $\rho$ is 0.

In this case, you have cylindrical symmetry, so try drawing a cross section of the surface through, say, the xz plane. You should be able to see pretty easily the limits of $\phi$, and you'll have to figure out the limits of $\rho$ as a function of $\phi$.

3. Nov 8, 2013

haruspex

Given the bounds, it might be easier to handle in cylindrical.