# How do you find the length of a curve defined parametrically?

##### 1 Answer
Sep 28, 2014

If the curve is defined by a parametric equations $\left\{\begin{matrix}x = x \left(t\right) \\ y = y \left(t\right)\end{matrix}\right.$, then the arc length $L$ of the curve from $t = a$ to $b$ can be found by

$L = {\int}_{a}^{b} \sqrt{{\left(\frac{\mathrm{dx}}{\mathrm{dt}}\right)}^{2} + {\left(\frac{\mathrm{dy}}{\mathrm{dt}}\right)}^{2}} \mathrm{dt}$.