Question

Find the area enclosed in the inner loop of the limacon, r = 2+costheta, and outside of the circle r=2

Answer 1

I think I figured it out but can someone check my work
2[1/2 the integral from 0 to π/2 of (2+costheta)^2 derivative of theta - 1/2 the integral from 0 to π/2 (4) derivative of theta }