I'm really stumped here as usual. Here is what i've managed to figure out.

I'm given two equations.

r=2

r=4cos(theta)

I converted them both to rectangular coordinates to get an idea of what the graph would look like.

I need to find either the area in red or the area in green.(In this case, I tried to find the area in green) .If I have the area in red or green, I know that I can just subtract one of them from pi*r^2 which in this case would be 4pi to get the area of the other section.

The problem I am facing right now is setting up the integral the proper way. I was thinking of going about it like this.

So a few questions. First, did I approach this in a correct way? Second, how would I know how to set this up to solve the integral using polar coordinates instead of converting it all to rectangular form?

Thanks for taking the time to answer, I tried to make this as clear as possible to see where i'm making my mistake or what I should be doing differently.