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WZ
Numerade Educator

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Problem 43 Hard Difficulty

Find the exact length of the curve.

$ x = t \sin t $, $ \quad y = t \cos t $, $ \quad 0\leqslant t \leqslant 1 $

Answer

$L=\int_{0}^{1} \sqrt{t^{2}+1} d t \stackrel{21}{=}\left[\frac{1}{2} t \sqrt{t^{2}+1}+\frac{1}{2} \ln (t+\sqrt{t^{2}+1})\right]_{0}^{1}=\frac{1}{2} \sqrt{2}+\frac{1}{2} \ln (1+\sqrt{2})$

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Video Transcript

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