_0^ 2n ( | x| - . | 1 2 x . | ) ;dx equals - Vidyadip

MCQ

$\int_0^{2n\pi } {\left( {|\sin x| - \left. {\left| {\frac{1}{2}\sin x} \right.} \right|} \right)} \;dx$ equals

A
$n$
✓
$2n$
C
$-2n$
D
None of these

✓

Answer

Correct option: B.

$2n$

b
(b) $\int_0^{2n\pi } {\left( {|\sin x| - \frac{1}{2}|\sin x|} \right)} \;dx$

$= \frac{1}{2}\int_0^{2n\pi } {\;\;\;\;|\sin x|dx} $

$ = \frac{{2n}}{2} \times 2\int_0^{\pi /2} {\sin x\;dx }$

$={ 2n} [ - \cos x]_0^{\pi /2} = 2n.$

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