Let $\mathbf { F } ( x , y , z ) = x \mathbf { i } + y \mathbf { j } + 2 z \mathbf { k }$ and let S be the boundary surface of the solid $E = \left\{ ( x , y , z ) \mid x ^ { 2 } + y ^ { 2 } \leq z \leq 4 \right\}$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .

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The Answer of Let $\mathbf { F } ( x , y , z ) = x \mathbf { i } + y \mathbf { j } + 2 z \mathbf { k }$ and let S be the boundary surface of the solid $E = \left\{ ( x , y , z ) \mid x ^ { 2 } + y ^ { 2 } \leq z \leq 4 \right\}$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .

Let F(x,y,z)=xi+yj+2zk\mathbf { F } ( x , y , z ) = x \mathbf { i } + y \mathbf { j } + 2 z \mathbf { k }F(x,y,z)=xi+yj+2zk

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