Let $\mathbf { F } ( x , y , z ) = x ^ { 2 } y \mathbf { i } - x ^ { 2 } z \mathbf { j } + z ^ { 2 } y \mathbf { k }$

Short Answer

Let $\mathbf { F } ( x , y , z ) = x ^ { 2 } y \mathbf { i } - x ^ { 2 } z \mathbf { j } + z ^ { 2 } y \mathbf { k }$ and let S be the surface of the rectangular box bounded by the planes $x = 0 , x = 3 , y = 0 , y = 2 , z = 0$ , and $z = 1$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .