Evaluate $\int _ { S } \vec { F } \cdot \vec { d A }$ , where $ { \vec { F } } = x \vec { i } + 6 y \vec { j }$ and S is the part of the cylinder $x ^ { 2 } + y ^ { 2 } = 4$ with x$\ge$0, y $\le$ 0, 0 $\ge$ z $\le$ 2, oriented toward the z-axis.

Question

Evaluate $\int _ { S } \vec { F } \cdot \vec  { d A }$ , where $  { \vec { F } } = x \vec { i } + 6 y \vec { j }$ and S is the part of the cylinder $x ^ { 2 } + y ^ { 2 } = 4$ with x$\ge$0, y $\le$ 0, 0 $\ge$ z $\le$ 2, oriented toward the z-axis.

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The Answer of Evaluate $\int _ { S } \vec { F } \cdot \vec  { d A }$ , where $  { \vec { F } } = x \vec { i } + 6 y \vec { j }$ and S is the part of the cylinder $x ^ { 2 } + y ^ { 2 } = 4$ with x$\ge$0, y $\le$ 0, 0 $\ge$ z $\le$ 2, oriented toward the z-axis.

Evaluate ∫SF⃗⋅dA⃗\int _ { S } \vec { F } \cdot \vec { d A }∫S​F⋅dA

Evaluate $\int _ { S } \vec { F } \cdot \vec { d A }$