Calculus

find the area of the region inside the limacon r= 8 + 4sin(theta)

HElp!! if you can show steps, i'd be greatful

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asked by KEvin
  1. for polar coordinates, dA = 1/2 r^2 dθ since each tiny wedge of area can be considered a sector of a circle of radius r and angle dθ.

    So, since

    r = 8+4sinθ,

    a = ∫[0,2π] 1/2 (8+4sinθ)^2 dθ
    now just expand the quadratic and evaluate each term, and you wind up with
    a = 72π

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    posted by Steve
  2. Find the area of the specified region.

    Inside the limacon r = 8 + 2 sin θ

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