Use the Divergence Theorem to Find the Flux of F $\iint _ { S } \mathbf { F } \cdot \mathbf { n } d S$

Short Answer

Use the Divergence Theorem to find the flux of F across S; that is, calculate $\iint _ { S } \mathbf { F } \cdot \mathbf { n } d S$ . $\mathbf { F } ( x , y , z ) = ( 9 x y + \cos z ) \mathbf { i } + ( x - \sin z ) \mathbf { j } + 4 x z \mathbf { k }$ ; S is the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$