_0^ /2 ( x - x) ( x + x) ,dx = - Vidyadip

MCQ

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

A
$ - 1$
B
$1$
✓
$0$
D
None of these

✓

Answer

Correct option: C.

$0$

c
(c) Put $\sin x + \cos x = t \Rightarrow - (\sin x - \cos x)dx = dt$

Also as $x = 0$ to $\frac{\pi }{2},t = 1$ to $1$.

Since here limit is $'1$ to $1'$,

therefore the value of integral will be zero,

$\left\{ \because \int_{a}^{a}{f(x)dx=0} \right\}$ .

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