d541c4…: “During the loud calculation”

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Let $F(x,y) = \sin (x)\cos (y)$ and $R = \{(x,y):0 \le x \le 2\pi , 0\le y\le \pi \}$ . Set-up an iterated integral that computes the surface area of the surface $z=F(x,y)$ over $R$ . $\iint _R \d S = \int _{\answer {0}}^{\answer {2\pi }} \int _{\answer {0}}^{\answer {\pi }} \answer {\sqrt {1+\cos ^2(x)\cos ^2(y) + \sin ^2(x)\sin ^2(y)}}\d y \d x$