Find the Flux Of Across the Surface of the Solid Bounded by the Paraboloid

question 60

Short Answer

Find the flux of $\mathbf { F } ( x , y , z ) = \left( y z ^ { 2 } \right) \mathbf { i } + \left( \mathrm { x } + y ^ { 3 } \right) \mathbf { j } + \left( z ^ { 3 } \right) \mathbf { k }$ across the surface of the solid bounded by the paraboloid $x = 4 - z ^ { 2 } - y ^ { 2 }$ and the $y z -$ plane.