Se cylindrical coordinates to evaluate the triple integral ∫∫∫ex2+y2−−−−−−√dv∫∫∫ex2+y2dv, where e is the solid bounded by the circular paraboloid z=1−4(x2+y2)z=1−4(x2+y2) and the xyxy -plane.

  note the extra factor of r comes from your specification of the  integral  of r d v . finally, we integrate over  z  from  z  = 0 , i.e., the x y plane, through to the top of the  solid  at  z  = 16 . we then need to  evaluate  the  integral. i'll reduce it to a single  integral  for you to  evaluate: 2 π 3  ∫  0 16 d  z  ( 4  − z  / 4 ) 3 / 2.