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. $\mathbf { F } ( x , y , z ) = x \mathbf { i } - z \mathbf { j } + y \mathbf { k } , \text { Sis the sphere } x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 25$ in the first octant,
with orientation toward the origin.