Triple integral w/ spherical subsitution

[dumbfoundead]

Homework Statement

f(x) is a differentiable function let
F(t)= \int\int\int_{x^2+y^2+z^2\leq t^2} f(x^2+y^2+z^2) dx dy dz

compute F^{'}(t)

Homework Equations

x=p sin \phi cos\theta
y= p sin \phi sin\theta
z= p cos \phi

spherical bounds 0<p<t 0<\phi<\Pi 0<\theta < 2\Pi

p^2 sin\phi = jacobian determinant

3. The attempt at a solution

carried through the substitution \int\int\int f(p^2) p^2 sin \phi dp d\phi d\theta

dont know how to evaluate \intf(p^2) sin\phi d\phi?

 

[Pengwuino]

Be careful about putting those repeated copies of the template in your questions.

The remaining integral is trivial. Your function is independent of \phi so the \phi integration is trivial; it's just the integral of sin(\phi)