c256eb…: “Ahead of the free group”

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Let $F(x,y) = 4$ and $R$ be the region enclosed by the petal of the rose curve $r=\sin (2\theta )$ in the first quadrant. Use polar coordinates to set-up and evaluate $\iint _R F(x,y) \d A$ . $\begin{align*} \iint_R F(x,y) \d A &= \int_{\answer{0}}^{\answer{\pi/2}}\int_{\answer{0}}^{\answer{\sin(2\theta)}} \answer{4r} \d r \d \theta\\ &= \answer{\pi/2} \end{align*}$