Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$

Short Answer

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , that is, find the flux of $\mathbf { F }$ across $S$ .
$\mathbf { F } ( x , y , z ) = - 4 z \mathbf { i } + y \mathbf { j } - 3 x \mathbf { k } ; \mathrm { S }$ is the hemisphere $z = \sqrt { 4 - x ^ { 2 } - y ^ { 2 } } ; \mathbf { n }$ points upward