Find the exact length of the polar curve.

r = theta^{2}

dr/dtheta = 2theta

r^{2}+(dr/dtheta)^{2}= theta^{2}+ 4 theta^{2} =5 theta^{2}

ds = √5 theta dtheta

integrating between 0 and 5pi/4

s = √5 * (5pi/4)^{2}/2= (25/32) *√5 pi^{2}

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