I am having trouble setting up the region of integration for a sphere centered at (0,0,1) with a radius of 1 using spherical coordinates. I know the upper bound for rho is 2cos(phi) but I cant figure out the lower bound.
P.S. I know there is a way to change to make (0,0,1) the new origin but I know that is not what I am supposed to do for this problem so would prefer to know some other way especially since the equation I am integrating is $\sqrt(x^2+y^2+z^2)$