How do you find the area of the region that lies inside the curves #r= 1+cos(theta)# and #r= 1-cos(theta)#?
First let us "see" our area:
Basically you want the area of the two loops enclosed by the two curves (vertically along the vertical axis).
In general the area in polar form is:
In this case let us start with the upper loop; you have:
area red shaded + area blue shaded
So you get:
Hope it helps (check my maths)