- #1
dumbfoundead
- 1
- 0
Homework Statement
f(x) is a differentiable function let
[itex]F(t)= \int\int\int_{x^2+y^2+z^2\leq t^2} f(x^2+y^2+z^2) dx dy dz [/itex]
compute F[itex]^{'}[/itex](t)
Homework Equations
x=p sin [itex]\phi[/itex] cos[itex]\theta[/itex]
y= p sin [itex]\phi[/itex] sin[itex]\theta[/itex]
z= p cos [itex]\phi[/itex]
spherical bounds 0<p<t 0<[itex]\phi[/itex]<[itex]\Pi[/itex] 0<[itex]\theta[/itex] < 2[itex]\Pi[/itex]
p^2 sin[itex]\phi[/itex] = jacobian determinant
3. The attempt at a solution
carried through the substitution [itex]\int\int\int f(p^2) p^2 sin \phi dp d\phi d\theta[/itex]
dont know how to evaluate [itex]\int[/itex]f(p^2) sin[itex]\phi[/itex] d[itex]\phi[/itex]?