Find the area common to the two circles x

^{2}+ y

^{2}= 4, x

^{2}+ y

^{2}= 6x.

Using polar coordinates I know the two equations of the circles are r=2 and r=6 cos(theta) respectively. What I tried to do was find the area over the x-axis first then double the result to provide the entire area.

What I thought would be this top area would be the sum of the double integrals from theta limits 0->acos(1/3) and r limits 6cos(theta)->4/6 for r dr d(theta)+ theta limits 0->acos(1/3) and r limits 4/6->2sin(theta) for r dr d(theta).

However I don't think this is right as both integrals provide a result that is either negative or too large to be the value within the designated area.