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Can someone please explain to me how to do this problem. I know you have to convert to polar coordinates. I found the bounds to be $\pm \frac {\pi}{3}$ & $3\le r \le 6 \cos \theta$.

Use a double integral to find the area of the region. The region inside the circle $(x − 3)^2 + y^2 = 9$ and outside the circle $x^2 + y^2 = 9$

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You already have the limits of integration. The only thing you need to do now is perform the integration. You want to do:

$$ \int_{-\pi/3}^{\pi/3}\int_3^{6\cos\theta}rdrd\theta $$

The $rdrd\theta$ bit just comes from the fact that this is what $dA$ is in polar coordinates.

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