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.

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The Answer of 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.

Compute ∫S(zi⃗+xj⃗+yk⃗)⋅dA→\int _ { S } ( z \vec { i } + x \vec { j } + y \vec { k } ) \cdot \overrightarrow { d A }∫S​(zi+xj​+yk)⋅dA

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