Question

Evaluate the integral ${\int }_{\pi }^{10\pi }\left|\sin x\right|dx$

• A. $20$
• B. $8$
• C. $10$
• D. $18$

Answer 1

The correct option is D $18$

For a periodic function $f\left(x\right)$ with period $a$,

${\int }_{ma}^{na}f\left(x\right)dx=(n-m){\int }_0^{a}f\left(x\right)dx$

Here , $f\left(x\right)=|\sin x|$ whose period is $\pi .$

Hence, ${\int }_{\pi }^{10\pi }|sinx|dx$

$=9{\int }_0^{\pi }|\sin x|dx$

$=9{\int }_0^{\pi }\sin xdx$ Since, $\sin x\ge 0\forall x\in [0,\pi ]$

$=9{[-\cos x]}_0^{\pi }$

$=18$

Hence, answer is option-(D).