Areas of regions Find the area of the following regions. In each case, graph the curve(s) and shade the region in question.
The region inside the limaçon r = 2 + cos θ and outside the circle r = 2
Given the limaçon r = 2+ cos θ
The equation (up to translation and rotation) of a limaçon in polar coordinate has the form
Therefore in our question we have and
Here since the limocon is a simple closed curve.
Also given a circle
The graph of the curve is