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

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 $\frac{\mathrm{dr}}{d \theta} = 1$, 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