The equations for the two circles are:
$r=18\cos{\theta}$
$r=3$
$r_f= 9$ and $r_g=3$
I can see that I need to subtract the $r=3$ circle, however im not sure on how to get the boundaries of integration. I set $18\cos{\theta} = 9$ and got $\pi/3$ and $5\pi/3,$ using these boundaries for the equation gives me a wrong number.
It seems like I need help on setting my boundaries. Thanks