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 vector field $\mathbf { F } ( x , y , z ) = - y \mathbf { i } + x \mathbf { j } + 3 z \mathbf { k }$ , where S is the hemisphere $z = \sqrt { 16 - x ^ { 2 } - y ^ { 2 } }$ with upward orientation.