Question

Set up the definite integral that represents the area of the region, inside r = 1 + cosθ but outside r= - cosθ

Answer 1

you know how the graph of each equation looks like?

Answer 2

http://www.wolframalpha.com/input/?i=r%3D1%2Bcos%5Ctheta
http://www.wolframalpha.com/input/?i=r%3D-cos%5Ctheta

Answer 3

first find theta where they cross:
-cosθ = 1 + cosθ
2cosθ=-1
cosθ=-1/2
θ=2Pi/3 and θ=4Pi/3

Answer 4

Now notice that the graph is siymetrical to x axis, so you only will need to take care of the upper part.
Split the integral in parts 1 and 2:

1º part is for 0<θ<Pi/2
2º part for Pi/2< θ <2Pi/3