triple integrals in spherical coordinates

Question

anonymous · Answer

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

anonymous · Answer

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

zepdrix · Answer

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? :)

anonymous · Answer

it just states that it is the unit ball

zepdrix · Answer

oh i see :)

anonymous · Answer

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

zepdrix · Answer

$$z= \rho \cos \phi$$$$x=\rho \cos \theta \sin \phi$$$$y=\rho \sin \theta \sin \phi$$
$$(x^2+y^2+z^2)=(\rho^2)$$
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).

zepdrix · Answer

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

anonymous · Answer

yeap its right thanks