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# Find the exact length of the curve.$x = t \sin t$, $\quad y = t \cos t$, $\quad 0\leqslant t \leqslant 1$

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

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

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#### Topics

Parametric Equations

Polar Coordinates

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp