How do you find the length of the polar curve r=theta ?

1 Answer
Wataru
Sep 7, 2014

If theta goes from theta_1 to theta_2, then the arc length of can be found by
L=int_{theta_1}^{theta_2}sqrt{theta^2+1}d theta.

Since r=theta, which gives {dr}/{d theta}=1, we have
L=int_{theta_1}^{theta_2}sqrt{r^2+({dr}/{d theta})^2}d theta =int_{theta_1}^{theta_2}sqrt{theta^2+1}d theta

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