Evaluate the surface integral $\int_S \mathbf{F} \cdot d\mathbf{S}$ where $\mathbf{F} = -xy\mathbf{i} + 8x^2 \mathbf{j} - yzk$ and $S$ is the surface $z = xe^y$, $0 \le x \le 1$, $0 \le y \le 1$, with upwards orientation. $\int_S \mathbf{F} \cdot d\mathbf{S} = $
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Since the surface is given by z = e, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, we can parameterize it as r(x, y) = xi + yj + ek, where 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Show more…
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