Question: Compute (iint_{mathcal{S}} mathbf{F} cdot d mathbf{S}) for the given oriented surface. (mathbf{F}=leftlangle x, y, e^{z}ightangle), cylinder (x^{2}+y^{2}=4,1 leq z leq 5), outward-pointing normal

Compute \(\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}\) for the given oriented surface.

\(\mathbf{F}=\left\langle x, y, e^{z}ightangle\), cylinder \(x^{2}+y^{2}=4,1 \leq z \leq 5\), outward-pointing normal 

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