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

Short Answer

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where S is the boundary surface of the region outside the sphere $\mathrm { x } ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1$ and inside the ball $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 4$ and $\mathbf { F } = e ^ { y ^ { 2 } } \mathbf { i } + \left( 5 y + e ^ { x ^ { 2 } } \right) \mathbf { j } + ( - 3 z + 2 x ) \mathbf { k }$ .