Convert the following integral to an equivalent integral in spherical coordinates.
Do NOT evaluate the integral.
∫∫∫ r^3 dz dr dtheta
limits of integration
p^2=x^2 +y^2 +z^2
The Attempt at a Solution
My problem is not converting the actual integrand but finding the new limits of integration. I realize that the theta limits will stay the same, but I am not sure how to find the rho or phi limits.
I have found through conversions that the new integrand will be
∫∫∫(p^5)sin(phi)^4 dp dphi dtheta