use double integral to find volume of the solid bounded by the paraboloid z=x^2+y^2 above, xy plane below, laterally by circular cylinder x^2 +(y-1)^2 = 1

So, I broke it above and below y-axis, and used polar: r varies from 0 to 2sin(theta) and theta varies from 0 to pi.

V = 2* integral from 0 to pi [[ integral from 0 to 2sin(theta) r^2 * r dr ]] dtheta

first integral results: 8sin^4(theta), second integral results: 3pi.

I think the answer is supposed to be 3pi/2. My limits are right??

checked my calculations:

integrate 2r^2 *r dr from 0 to 2sinx - Wolfram|Alpha

integrate 8sin^4(x) from 0 to pi - Wolfram|Alpha