${\int }_{\mathrm{\pi }}^{10\mathrm{\pi }} |\sin \mathrm{x}|\mathrm{dx}=$

For a periodic function f(x) with period a,
$\text{ Here, }f\left(x\right)=|\sin x|\text{ whose period is }\pi \text{. }$

$\text{ Hence, }{\int }_{\pi }^{10\pi } |\sin x|dx$$\begin{array}{l}=9{\int }_0^{\pi } |\sin x|dx\\ =9{\int }_0^{\pi } \sin xdx\\ =9[-\cos x{]}_0^{\pi }\\ =18\end{array}$
${\int }_{\mathrm{\pi }}^{10\mathrm{\pi }} |\sin \mathrm{x}|\mathrm{dx}={\int }_0^{9\mathrm{\pi }} |\sin \mathrm{x}|\mathrm{dx}=18$