the question is
Use polar coordinates to find the volume of the solid which is under the paraboloid and above the disk in the plane .
If then so we integrate over the circle as the radius goes from 0 to 3 and all the way round the circle or just 4 times the part in the first quadrant since f is symmetrical:
and you can check that by just calculating the volume inside the paraboloid via shells and then subtract that from just the cylinder it's housed in:
half-in and half-out right?