I am having a problem solving this integration by changing to polar coordinates.
Blockquote$$\int\limits_{0}^{2}\int\limits_{1}^{\sqrt{2x-x^2}}\dfrac{x}{\sqrt{x^2+y^2}}~dy~dx$$
As $y=\sqrt{2x-x^2}$ is the equation of circle centered at $(1,0)$ and has a radius $1$. The limit of $y$ is $1\leq y \leq \sqrt{2x-x^2}$, so the vertical lines enter through the line $y=1$ and leave the circle at the same point.
I am not able to draw the region.