6. Length of the Polar Curve

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NOBFAVPU21

Mathematics

Description

Find the exact length of the polar curve.

r = θ2,    0 ≤ θ ≤ 5π/4

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Explanation & Answer

r = theta2

dr/dtheta = 2theta

r2+(dr/dtheta)2= theta2+ 4 theta2 =5 theta2

ds = √5 theta dtheta

integrating between 0 and 5pi/4

s = √5 * (5pi/4)2/2= (25/32) *√5 pi2   



Anonymous
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