Find the exact length of the polar curve.
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
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