Use polar coordinates to evaluate the double integral $\iint_R2ydA$. $R$ is the region in the first quadrant bounded above by $x^2−2x+y^2=0$ and below by the line $y=x$.
I have determined the limit of $\theta$, which is $\pi/4$ by using the equation $r\sin(\theta)=r\cos(\theta)$. But how to find the limit of the radius? Is the radius simply $0$ to $1$? This is a circle with a radius of $1$ unit shifted to the right by $1$ unit after completing the square. Thanks.