Use a double integral to find the area of the region.
The region inside the circle $(x-1)^2+y^2=1$ and outside the circle $x^2+y^2=1$.
I'm pretty sure my inner integral is going to be $\int_1^{2\cos \theta} r\,dr$ but I'm not sure what to put for my outer integral when integrating with respect to $\theta$. I can see in my notes theres a line tangent to the circle I'm integrating but I'm not sure how to get the exact $\pi$ value that touches it, I can only guess, but my drawing is bad so its hard to guess. The book doesn't really say with this type of problem. I think I also remember my teacher saying I could subtract two equations to get the inner integral but I'm not sure. So how to I set the boundaries and solve?
Guide:
Find the intersection point between the two curve.
$$x^2+y^2=1$$ $$(x-1)^2+y^2=1$$
After you find the intersection, $(x,y)$, you can use $\cos^{-1}(x)$ to obtain the corresponding angle.
Edit:
Expanding the second equation $$x^2+y^2-2x+1=1,$$
substitute the first equation into the second equation and solve for $x$.