Answer
$\frac{\pi}{4}-\frac{1}{2}ln2$
Work Step by Step
=$\int\int_R\frac{y}{x^2y^2+1}dA$
=$\int_{0}^{1}\int^{1}_{0}\frac{y}{(xy)^2+1}dx dy$
=$\int^{1}_{0}[tan^{-1}(xy)]^1_0dy$
=$\int^{1}_{0}tan^{-1}ydy$
=$[y tan^{-1}y-\frac{1}{2}ln|1+y^2|]$
=$\frac{\pi}{4}-\frac{1}{2}ln2$
