# What is the arclength of f(x)=xsin3x on x in [3,4]?

Jul 9, 2018

$\approx 6.578961133$

#### Explanation:

Given is
$f \left(x\right) = x \sin \left(3 x\right)$
We Need the product and the chain rule:

$f ' \left(x\right) = \sin \left(3 x\right) + 3 x \cos \left(3 x\right)$ so we have evaluate the following integral

${\int}_{3}^{4} \sqrt{1 + {\left(\sin \left(3 x\right) + 3 x \cos \left(3 x\right)\right)}^{2}} \mathrm{dx}$
a numerical method gives us

$\approx 6.578961133$