Question

Find the area A inside
r = 1 + cos θ
and outside
r = cos θ

Answer 1

The total area is given by the integral
\[\large2\cdot\left[\frac{1}{2}\int_0^{\pi}\left((1+\cos\theta)^2-(\cos\theta)^2\right)\;d\theta\right]\]
The 2 comes from the fact that the curves are symmetric across the x-axis.