81c4cb…: “As per a free trapezoid”

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Let $F(x,y) = 1-x^2-y^2$ and $R$ be the region enclosed by the circle $x^2+y^2=1$ . Use polar coordinates to set-up and evaluate $\iint _R F(x,y) \d A$ . $\begin{align*} \iint_R F(x,y) \d A &= \int_{\answer{0}}^{\answer{2\pi}}\int_{\answer{0}}^{\answer{1}} \answer{(1-r^2)r} \d r \d \theta\\ &= \answer{\pi/2} \end{align*}$