changing an integral from rectangular to spherical

I have a triple integral in terms of x,y and z and need to convert it to spherical coordinates.

it is the integral from 0 to 2 and then from 0 to (4 - x^2)^(1/2) inner bounds from 0 to (4 - x^2 - y^2)^(1/2) of (x^2 + y^2 + z^2)^(1/2) dz dy dx

Since the integral is of roe spherical will work well I think!!!

So, we will integrate roe^3 sin phi d roe d phi d theta

My lower bounds must be all zeros.

Can someone please go through the thinking process to determine my upper bounds?

Once I have these I can do the integration no problem. Without them I am stuck! Frostking