e4ae50…: “Into the red equation”

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Let $F(x,y) = \ln (x^2+y^2)$ and $R$ be the annulus enclosed by the circles $x^2+y^2=1$ and $x^2+y^2=4$ . Use polar coordinates to set-up and evaluate $\iint _R F(x,y) \d A$ . $\begin{align*} \iint_R F(x,y) \d A &= \int_{\answer{0}}^{\answer{2\pi}}\int_{\answer{1}}^{\answer{2}} \answer{\ln(r^2)r} \d r \d \theta\\ &= \answer{2\pi (\ln(16)-3/2)} \end{align*}$