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For the curve r = 2 sin 3(theta):

Find the arc length of one petal

1 answer

ds = √(r^2 + r'^2)
r' = 6cos3θ

s = ∫[0,π/3] √(4sin^2(3θ) + 36cos^2(3θ)) dθ
= 2∫[0,π/3] √(1 + 8cos^2(3θ)) dθ

This is an elliptic integral. Good luck.
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