Evaluate the Flux Integral $\iint _ { S } ( 2 x \mathbf { i } - y \mathbf { j } + 3 z \mathbf { k } ) \cdot \mathbf { n } d S$

Short Answer

Evaluate the flux integral $\iint _ { S } ( 2 x \mathbf { i } - y \mathbf { j } + 3 z \mathbf { k } ) \cdot \mathbf { n } d S$ over the boundary of the ball $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 9$ .