A cardioid r=1+cos(theta)

Question

A circle r=3*cos(theta)

a) Define the domain of the region enclosed inside both the cardioid and the circle.

b) Use polar coordinates to calculate the area.

(We can use symmetry about x-axis)

Answer 1

May I suggest two excellent videos from the
Khan Academy
The first develops the standard method of finding the area
https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/area-polar-graphs/v/formula-area-polar-graph

And the second just about matches your question
https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/area-polar-graphs/v/cardioid-area

Answer 2

The videos did help but i still have trouble setting up the integrals. Since this is part of double integrals section in my course... i'm trying to do it in the form of double integrals.

Is this correct?

Outer integral is from -pi/2 to pi/2

Inner is [r dr d(theta)] from 3*cos(theta) to 1+cos(theta) ?

thanks