Question

Find the volume that is restricted by paraboloid z = 2x^2 +2y^2 -8 and xy-plane using polar coordinates.

Answer 1

start by changing to polar

Answer 2

V = \(\large \int \int_R z ~dx dy\)

u need to convert z, differentials, and bounds to polar..

Answer 3

\(x = r\cos \theta\)
\(y = r\sin \theta\)


convert z to polar, wat do u get ?

Answer 4

\[2r ^{2} -8\]

Answer 5

yes, next think a bit how the projection of paraboloid look in xy-axis