Question

Evaluate :${\int }_0^{10\pi }|\sin x|dx$

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

Answer 1

The correct option is A

$20$

Evaluating the integral :

The period of $\left|\sin \right(x\left)\right|$ is $\mathrm{\pi }$

$\Rightarrow 10{\int }_0^{\pi }\left|\sin \right(x\left)\right|dx$

$sin\left(x\right)$ is always positive when $0<x<\mathrm{\pi }$ then $\left|\sin \right(x\left)\right|$ $=sin\left(x\right)$

$\Rightarrow 10{\int }_0^{\pi }\sin \left(x\right)dx$

$\Rightarrow 10{\left[-\cos \left(x\right)\right]}_0^{\mathrm{\pi }}$

$$\begin{gathered} \Rightarrow -10\cos \left(\mathrm{\pi }\right)+10\cos \left(0\right) \\ \Rightarrow 20[\therefore \cos (\mathrm{\pi })=-1,\cos (0)=1] \end{gathered}$$

Hence, option (A) is the correct answer.