afaf90…: “Of the noisy parallelogram”

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Let $F(x,y) = 3x-7y$ and $R$ be the rectangle with opposite corners $(-1,0)$ and $(1,3)$ . Set-up an iterated integral that computes the surface area of the surface $z=F(x,y)$ over $R$ . $\iint _R \d S = \int _{\answer {-1}}^{\answer {1}} \int _{\answer {0}}^{\answer {3}} \answer {\sqrt {59}}\d y \d x$

Compute the iterated integral above. $\iint _R \d S = \answer {6\sqrt {59}}$