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

Short Answer

Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ for the given vector field F and the oriented surface S. In other words, find the flux of F across S. $\mathbf { F } ( x , y , z ) = 9 x \mathbf { i } + 3 y \mathbf { j } + 6 z \mathbf { k }$ $S \text { is the cube with vertices } ( \pm 1 , \pm 1 , \pm 1 ) \text {. }$