Compute $\int _ { S } ( z \vec { i } + x \vec { j } + y \vec { k } ) \cdot \overrightarrow { d A }$

Short Answer

Compute $\int _ { S } ( z \vec { i } + x \vec { j } + y \vec { k } ) \cdot \overrightarrow { d A }$ , where S is oriented in the positive $\vec { j }$ direction and given, for 0 $\le$ s $\le$ 1, 0 $\le$ t $\le$ 2, by x = s, y = t², z =8 t.