2d3vljtq

2022-07-06

What is the arclength of $f\left(x\right)=x\mathrm{sin}3x$ on $x\in \left[3,4\right]$?

Kaya Kemp

Expert

Given is
$f\left(x\right)=x\mathrm{sin}\left(3x\right)$
We Need the product and the chain rule:
${f}^{\prime }\left(x\right)=\mathrm{sin}\left(3x\right)+3x\mathrm{cos}\left(3x\right)$ so we have evaluate the following integral
${\int }_{3}^{4}\sqrt{1+\left(\mathrm{sin}\left(3x\right)+3x\mathrm{cos}\left(3x\right){\right)}^{2}}dx$
a numerical method gives us
$\approx 6.57$

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