A limacon is given by r=1+2cosθ. The curve has an inner loop.
(a) Find the values of θ at which the curve passes through the pole (the origin).
(b) Write a definite integral that represents the area enclosed by the inner loop of the limacon. Be sure to specify the limits of integration.
(c) Evaluate the integral from part (b) to determine the exact area of the inner loop.