_0^ /2 , , , , ,| x - x| ,dx = - Vidyadip

MCQ

$\int_0^{\pi /2} {\,\,\,\,\,|\sin x - \cos x|\,dx = } $

A
$0$
✓
$2(\sqrt 2 - 1)$
C
$\sqrt 2 - 1$
D
$2(\sqrt 2 + 1)$

✓

Answer

Correct option: B.

$2(\sqrt 2 - 1)$

b
(b) $\int_0^{\pi /2} {\,\,\,\,|\sin x - \cos x|dx} $

$ = \int_0^{\pi /4} { - (\sin x - \cos x} )dx + \int_{\pi /4}^{\pi /2} {\,(\sin x - \cos x)dx} $

$= 2(\sqrt 2 - 1)$.

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