Question

$\underset{0}{\overset{2\pi }{\int }}|\sin x|dx=$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (D)

$I=\underset{0}{\overset{2\pi }{\int }}|\sin x|dx=2\underset{0}{\overset{\pi }{\int }}|\sin x|dx$
$\because f(2\pi -x)=f(x)$
$=4\underset{0}{\overset{\pi /2}{\int }}|\sin x|dx=4\underset{0}{\overset{\pi /2}{\int }}\sin xdx=4[-\cos x{]}_0^{\pi /2}$
$=4(-0+1)=4$