Thread: Integration using polar coordinates

Hey I am having trouble with another integral problem:
Use polar coordinates to find the volume of the region between the plane z = 0 and
the surface z = sqrt(x2 + y2) inside of the cylinder x2 + y2 = 2x.

I did the problem already but am doubtful of my answer. The way i set up the triple integral was i took the integral of r, from dzdrdtheta. z(from 0 to r), r(from 0 to 2cos(theta)), theta(from 0 to 2pi)
I got 0 as the answer, which doesnt seem correct.

Actually, is the range of theta (-pi/2 to pi/2)?