Question

Find the volume of the solid W bounded above by the paraboloid z=9−x^2−y^2, below by the xy-plane, and that lies within the cylinder x^2+y^2=4.

help
i know that if i use cylindrical coord
then
r^2 = 4/..... r=1
theta= 0, 2pi
z= 9-r^2

Answer 1

below xy-plane?

Answer 2

bounded below by the xy-plane\[\int\limits_{-2}^{2}\int\limits_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}}\int\limits_{0}^{9-x^2-y^2} dz \: dy \: dx\]switch to cylindrical coordinates\[\int\limits_{0}^{2\pi}\int\limits_{0}^{2}\int\limits_{0}^{9-r^2} r \: dz \: dr \: d \theta\]