# How do you find the arc length of the curve y=xsinx over the interval [0,pi]?

Mar 21, 2018

Find ${\int}_{0}^{\pi} \sqrt{1 + {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^{2}} \mathrm{dx}$

#### Explanation:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \sin x + x \cos x$, so we need

${\int}_{0}^{\pi} \sqrt{1 + {\left(\sin x + x \cos x\right)}^{2}} \mathrm{dx}$ which is about $5.04$