Calculus

Find the area of one petal of the polar curve r = 3 cos 3θ. (4 points)

A) 7 times pi over 12
B) 3 times pi over 4
C) 11 times pi over 12
D) 2π

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  1. one petal has -π/6 ≤ θ ≤ π/6
    Using the symmetry of the curve, the area is
    A = 2∫[0,π/6] 1/2 r^2 dθ = ∫[0,π/6] 9 cos^2(3θ)
    = 9/2 ∫[0,π/6] 1+cos(6θ) dθ
    Now finish it off

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    oobleck

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