Let ${ \vec { F } } = x \vec { i } + 5 y \vec { j } + z \vec { k }$ and S be parametric surface $\vec { r } ( s , t ) = s \vec { i } + t \vec { j } + ( 4 s + t - 4 ) \vec { k } , \quad 0 \leq s \leq 1,0 \leq t \leq 2$ oriented upward.
Use the formula for a flux integral over a parametric surface to find $\int _ { S } \vec { F } \cdot d \vec { A }$ .

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The Answer of Let ${ \vec { F } } = x \vec { i } + 5 y \vec { j } + z \vec { k }$ and S be parametric surface $\vec { r } ( s , t ) = s \vec { i } + t \vec { j } + ( 4 s + t - 4 ) \vec { k } , \quad 0 \leq s \leq 1,0 \leq t \leq 2$ oriented upward.
Use the formula for a flux integral over a parametric surface to find $\int _ { S } \vec { F } \cdot d \vec { A }$ .

Let F⃗=xi⃗+5yj⃗+zk⃗{ \vec { F } } = x \vec { i } + 5 y \vec { j } + z \vec { k }F=xi+5yj​+zk

Let ${ \vec { F } } = x \vec { i } + 5 y \vec { j } + z \vec { k }$