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Calculus 2

Consider the polar curve: r=3cos(3ϴ)
a) Find the area of the first leaf of the graph.

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  1. taking advantage of symmetry, and knowing that
    r(0)=3
    r(π/6)=0
    all we have to do is double the area for that domain.

    a = 2∫[0,π/6] 1/2 r^2 dθ = ∫[0,π/6] 9cos^2(3θ) dθ = 3π/4

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