_0^ /2 x x + x ,dx equals - Vidyadip

MCQ

$\int_0^{\pi /2} {\frac{{\sin x}}{{\sin x + \cos x}}\,dx} $ equals

A
$\frac{\pi }{2}$
B
$\frac{\pi }{3}$
✓
$\frac{\pi }{4}$
D
$\frac{\pi }{6}$

✓

Answer

Correct option: C.

$\frac{\pi }{4}$

c
(c) $I = \int_0^{\pi /2} {\frac{{\sin x.dx}}{{\sin x + \cos x}}} = \int_0^{\pi /2} {\frac{{\cos x.dx}}{{\cos x + \sin x}}} $,

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

$2I = \int_0^{\pi /2} {dx} \Rightarrow I = \frac{\pi }{4}$.

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