Question

find the volume below the surface z=x^2+y^2 above z=0 and inside the cylinder x^2+y^2=2y
(ANSWER=3π/2)

Answer 1

switch to cylindrical coordinates

Answer 2

integral from 0 -> 2PI
integral from 0-> root2
x^2+y^2
\[\int\limits_{0}^{2\pi}\int\limits_{0}^{\sqrt{2}}zrdrd \theta \]

Answer 3

be carefull, paraboloid and cilinder are not concentrical

Answer 4

\[\iiint 1 dV\]

Answer 5

why integral 0 to 2π

Answer 6

Oh thats a good point @myko
center of shadow in xy plane gets shifted to (0, 1)

Answer 7

x^2+y^2=2y

x^2 + (y-1)^2 = 1