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

Solution 20RE

Step 1:

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

Step 2:

The graph of the curve is