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

Short Answer

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where $\mathbf { F } ( x , y , z ) = - y \mathbf { i } + x \mathbf { j } + 2 z \mathbf { k }$ and S is the upper half of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 25$ , with upward orientation.