Question

$\underset{0}{\overset{10\pi }{\int }}|\sin x|dx$ is:

• A. 20
• B. 8
• C. 10
• D. 18

Answer 1

Answer: (A)

The period of $|\sin x|$ is $n$ .
$\underset{0}{\overset{10\pi }{\int }}|\sin x|dx$
$=\left[\underset{0}{\overset{\pi /2}{\int }}\sin xdx+\underset{\pi /2}{\overset{\pi }{\int }}\sin xdx\right]$
$=10[-\cos x{]}_0^{\pi /2}+[-\cos x{]}_{\pi /2}^{\pi }$
Alternative Solution:
$\therefore$ Required area $=10\underset{0}{\overset{\pi }{\int }}\sin xdx$
$=10[-\cos x{]}_0^{\pi }=-10(\cos \pi -\cos 0)=20$