Calculus
posted by Mackenzie .
Evaluate the integral by changing to spherical coordinates.
The outer boundaries are from 0 to 1.
The middle one goes from sqrt(1x^2) to sqrt(1x^2)
The inner one goes from sqrt(1x^2z^) to sqrt(1x^2z^)
for 1/sqrt(x^2+y^2+z^2) dydzdx
I don't understand how to get the limits of integration. I know for rho it will be from 0 to 1. I want to know the process to get the boundaries for phi and theta since I have a few other similar problems to do.

you are integrating over the whole sphere, so
0 <= p <= 1 (insideoutside)
0 <= φ <= 2π (whole xy plane)
0 <= θ <= π (toptobottom of sphere)
There must be some examples in your text. And there are surely some online. 
The solution says the the boundary for phi is from 0 to pi as well as the one for theta.

I'd have to think about it, but you obviously have both halves of the circle and both halves of the sphere.