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

  • Math - ,

    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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