Find the volume of the region bounded in back by the plane x=0 , on the front
and sides by the parabolic cylinder x=1−y2 , on top by the paraboloid z=x2+y2 , and on the
bottom by the xy-plane. Find the volume of the region bounded in back by the plane x=0 , on the front
and sides by the parabolic cylinder x=1−y2 , on top by the paraboloid z=x2+y2 , and on the
bottom by the xy-plane. @Mathematics

Question

turingtest · Answer

Bounded in back by $x=0$ and in front by $1-y^2$$$0\le x\le1-y^2$$this suggeests that$$0\le y\le1$$since it is bounded below by the xy-plane, $z\ge0$ so we have$$0\le z\le x^2+y^2$$I think from here we want to convert this to cylindrical coordinates