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