## Converting unit square domain in (x,y) to polar coordinates

I have the following double integral \int_{0}^{1}\int_{0}^{1}\frac{x}{\sqrt{x^2+y^2}}dxdy The integrand is fairly simple: \frac{x}{\sqrt{x^2+y^2}}dxdy=\frac{r\cos(\theta )}{\sqrt{r^2}}rd\theta{}dr=r\cos{(\theta)}d\theta{}dr My trouble is with the limits of integration. I’ve tried: 0 \leq y \leq 1 means 0 \leq{} r\sin(\theta{}) \leq 1 so 0 \leq \theta \leq arcsin(1/r) But why isn’t it just 0<\theta < \pi{}/2 since the unit square is in … Read more