Posted by **Cole** on Monday, June 24, 2013 at 7:15pm.

Find the area shared by the cardioids r=6(1+cos(theta)) and r=6(1-cos(theta))

- Math -
**Steve**, Tuesday, June 25, 2013 at 10:10am
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

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