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

Short Answer

Compute the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ if $\mathbf { F } ( x , y , z ) = z ^ { 2 } \mathbf { k }$ and S is the piece of the sphere $z ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1$ in the second octant $( x \leq 0 , y \geq 0 , z \geq 0 )$ .