Find the area of the region between the circles x^2 + y^2 = 4 and x^2 + y^2 = 4x

My attempt at the solution:

I found the points of intersection are at (1,-sqrt(3)) and (1, sqrt(3))

Then I solved for x in each equation:

x=sqrt(4-y^2) , x=sqrt(y^2+4) + 4

This is where I get stuck. I don't know where to go from here. Can someone please give me a hint or suggestion? Also, is what I Have so far correct?