# Double Integral Polar

Tags:
1. Dec 1, 2017

1. The problem statement, all variables and given/known data
r=1 and r=1+cos(theta), use a double integral to find the area inside the circle r=1 and outside the cardioid r=1+cos(theta)

2. Relevant equations

3. The attempt at a solution
I am confused on the wording and how to set it up. I tried setting it up by setting theta 0 to pi. and r as 1 to 1+cos(theta). I used r drd(theta) as the equation to use.

2. Dec 1, 2017

### BvU

Make a picture !

3. Dec 1, 2017

I did make a picture I am confused by the little piece of the cardoid that isn't in the first quadrant.

4. Dec 1, 2017

### Ray Vickson

In the whole plane, what is the region outside the cardioid? What is the region inside the circle? What is the intersection of those two regions?

Last edited: Dec 1, 2017
5. Dec 2, 2017

### Staff: Mentor

As shown in BvU's graph, the region of integration is entirely on the left side of the vertical axis. What is $\theta$ at the upper intersection point? At the lower intersection point? There is also some symmetry you can take advantage of.

6. Dec 3, 2017

### BvU

Ambiguous -- in the picture a small piece is missing because I simply didn't grab the full $\theta$ range for the red curve