Question

$\underset{0}{\overset{20\pi }{\int }}(|\sin x|+|\cos x|{)}^{2}dx$ is equal to :-

• A. $10(\pi +4)$
• B. $10(\pi +2)$
• C. $20(\pi -2)$
• D. $20(\pi +2)$

Answer 1

Answer: (D)

$I=\underset{0}{\overset{20\pi }{\int }}(|\sin x|+|\cos x|{)}^{2}dx;$ ( Jack property)
$I=40\underset{0}{\overset{\pi /2}{\int }}(\sin x+\cos x{)}^{2}dx$
$I=40\underset{0}{\overset{\pi /2}{\int }}(1+\sin 2x)dx$
$I=20[\pi +2]$