How to evaluate $\displaystyle\int_{-1}^{1}\int_{-\sqrt{1-y^2}}^{0}\frac{dxdy}{1+x^2+y^2}$
This is my steps :
$\displaystyle\begin{align*}\int_{-1}^{1}\int_{-\sqrt{1-y^2}}^{0}\frac{dxdy}{1+x^2+y^2}&=\frac{1}{2}\int_{0}^{2\pi}\int_{-1}^{0}\frac{r}{1+r^2}drd\theta\end{align*}$
Is that right?