I have a function $f(x,y) = x$, and I want to find the double integral over the circular region $(x-2)^2 + y^2 =1 $ using polar coordinates.
Converting the region to polar, we get
$r^2 -4cos\theta r + 3 = 0$
Solving for $r$ gives me the limits for $r$ in the integral:
$r = 2 cos\theta + \sqrt{4cos^2\theta -3}$
$r = 2 cos\theta - \sqrt{4cos^2\theta -3}$
My question is how do I find the limits for $\theta$?