5b984f…: “Onto the red tetrahedron”

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Let $F(x,y) = (x-y)/(x+y)$ and $R$ be the region enclosed by the lines $y=x$ , $y=0$ , and the circle $x^2+y^2=1$ in the first quadrant. Use polar coordinates to set-up and evaluate $\iint _R F(x,y) \d A$ . $\begin{align*} \iint_R F(x,y) \d A &= \int_{\answer{0}}^{\answer{\pi/4}}\int_{\answer{0}}^{\answer{1}} \answer{(\frac{\cos(\theta)-\sin(\theta)}{\cos(\theta)+\sin(\theta)})r} \d r \d \theta\\ &= \answer{\ln(2)/4} \end{align*}$