## math_proof 2 years ago triple integrals in spherical coordinates

1. math_proof

$\int\limits_{}^{}\int\limits_{}^{}\int\limits_{}^{}(x^2+y^2+z^2)^{5/2}$

2. math_proof

i know it going to be p^5 but what will the ingtegrals be

3. zepdrix

Do we have a region we're integrating over? D: Any boundaries like z=0, x=0 or anything? :O Or you're more concerned with just converting it correctly right now? :)

4. math_proof

it just states that it is the unit ball

5. zepdrix

oh i see :)

6. math_proof

so i guess the theta will be from 0 to 2pi right?

7. zepdrix

$z= \rho \cos \phi$$x=\rho \cos \theta \sin \phi$$y=\rho \sin \theta \sin \phi$ $(x^2+y^2+z^2)=(\rho^2)$ Oh oh you said you already figured that part out :) my bad. Yah theta will range from 0 to 2pi. Phi from 0 to pi I think... and Rho from 0 to our radius (1 since it's the UNIT ball).

8. zepdrix

$\huge \int\limits_{\theta=0}^{2\pi}\int\limits_{\phi=0}^{\pi}\int\limits_{\rho=0}^{1}\rho^5 (\rho^2 \sin \phi d \rho d \phi d \theta)$ Somethinggggg like that. Thinkinggg..

9. math_proof

yeap its right thanks