Question

The value of ${\int }_0^{2\pi }\left|\sin x\right|dx$ is

• A. $0$
• B. $6$
• C. $4$
• D. $8$

Answer 1

Answer: (C)

$4$

${\int }_0^{2\pi }\left|\sin x\right|dx={\int }_0^{\pi }\sin xdx+{\int }_{\pi }^{2\pi }-\sin xdx$

${\int }_0^{2\pi }\left|\sin x\right|dx=-\cos x{]}_0^{\pi }+\cos x{]}_{\pi }^{2\pi }$

${\int }_0^{2\pi }\left|\sin x\right|dx=-\cos \pi +cos0+\cos 2\pi -\cos \pi$

${\int }_0^{2\pi }\left|\sin x\right|dx=-(-1)+1+1-(-1)=4$