A cardioid is described by r=2(1+cosθ), and a circle is described by r=2. Let R be the region that is inside the cardioid and outside the circle.
(a) Solve for all θ in [0,2π) at which the two curves intersect.
(b) Express the area of R as a definite integral or sum of definite integrals, making clear the limits of integration for each piece.
(c) Evaluate the integral expression in part (b) to obtain the exact area of R.