# Homework Help: Integrating over a sphere

1. Nov 5, 2013

### PsychonautQQ

1. The problem statement, all variables and given/known data
Triple Integral: x^2+y^2+z^2dV over the ball x^2+y^2+z^2 ≤ 9

2. Relevant equations

3. The attempt at a solution
so With my integral I had
Triple Integral: p^3sin∅dpd∅dθ
0≥p≥3
0≥∅≥∏
0≥θ≤2∏

Does this look like the correct integral? I swear it is! Yet my answer is wrong. I rebuke these foul math gods!!

2. Nov 5, 2013

### pasmith

$$\iiint_{r \leq 3} r^2\,dV = \int_0^{2\pi} \int_0^{\pi} \int_0^3 (r^2) (r^2 \sin \theta) \,dr\,d\theta\,d\phi$$

3. Nov 5, 2013

### haruspex

That looks to me the same as PsychonautQQ posted, just with some of the ≤/≥ turned around the right way and with theta and phi swapped.
PsychonautQQ, what answer do you get and what is it supposed to be? Pls post your working in solving the integral.

4. Nov 5, 2013

### pasmith

And the correct expression for the volume element ...

5. Nov 5, 2013

### haruspex

Ah yes - the extra r factor.