Calculate integral $\displaystyle-\frac{1}{2\pi i}\int_{B(z_0,r)}\frac{1}{w-z}\mathrm d \bar w\mathrm d w$, where $B(z_0,r)$ is any ball in upper-plane, $z\in B(z_0,r)$.
If $z\notin B(z_0,r)$, I can work out it with result $r^2/(z-z_0)$, but if $z\in B(z_0,r)$, the result is $\bar z-\bar {z_0}$, I have no idea how to solve it. Thanks for any help!