Description
Find the exact length of the polar curve.
r = 3 sin θ, 0 ≤ θ ≤ π/4
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Explanation & Answer
r = 3 sin theta
dr/dtheta = 3 cos theta
r2+(dr/dtheta)2 = 32 sin 2 theta+ 32 cos 2 theta = 9
ds = √9 d theta
ds = 3 d theta
integrating between 0 and pi /4s = 3 * pi/4 = 3/4 pi
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