_ 0 ^ 20 (| x|+| x|)^ 2 d x is equal to. - Vidyadip

MCQ

$\int_{0}^{20 \pi}(|\sin x|+|\cos x|)^{2} d x$ is equal to.

A
$10(\pi+4)$
B
$10(\pi+2)$
C
$20(\pi-2)$
✓
$20(\pi+2)$

✓

Answer

Correct option: D.

$20(\pi+2)$

d
$I=\int_{0}^{20 \pi}(|\sin x|+|\cos x|)^{2} d x \quad ;($ Jack property $)$

$I=40 \int_{0}^{\pi / 2}(\sin x+\cos x)^{2} d x$

$I=40 \int_{0}^{\pi / 2}(1+\sin 2 x) d x$

$I=20[\pi+2]$

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