Correct Answer - Option 3 : π/4
Concept:-
By the properties of definite integral –
\(\mathop \smallint \limits_b^a f\left( x \right)dx = \frac{{upper\;limit - lower\;limit}}{2}\)
\(\mathop \smallint \limits_b^a f\left( x \right)dx = \frac{{a - b}}{2}\;\; - - - \left( 1 \right)\)
Calculation:
Given,
Using equation (1)
Given, \(\mathop \smallint \limits_0^{\pi /2} \frac{{\sin x}}{{\sin x + \cos x}}dx\)
Using equation (1) \(\mathop \smallint \limits_0^{\pi /2} \frac{{\sin x}}{{\sin x + \cos x}}dx = \frac{{\frac{\pi }{2}\; - \;0}}{2}\)
\( = \frac{\pi }{4}\)
