7f730b…: “Left of the gold city”

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Let $R=\{(x,y):0\le x\le 1, 0\le y\le 1\}$ and $F : \R ^2 \to \R$ be the function defined by the rule $F(x,y) = xy.$ Evaluate $\iint _R F \d A$ .

$\iint _R F \d A = \answer {1/4}.$

Let $S=\{(x,y,z):0\le x\le 1, 0\le y\le 1, 0\le z\le 1\}$ and $G : \R ^3 \to \R$ be the function defined by the rule $G(x,y) = xyz.$ Evaluate $\iiint _S G \d V$ .

$\iiint _S G \d V = \answer {1/8}.$