Posted by Cole on .
Find the area shared by the cardioids r=6(1+cos(theta)) and r=6(1-cos(theta))
The curves intersect when θ= π/2,3π/2
By symmetry, then the area is
a = 2∫[π/2,3π/2] 1/2 (6(1-cosθ))^2 dθ
= 36∫[π/2,3π/2] 1 - 2cosθ + cos^2θ dθ
= 9(6θ-8sinθ+sin2θ) [π/2,3π/2]
= 4 + 3π/2