PrepRung
Sign inSign up free

JEE Main 2016 · Mathematics · Indefinite and Definite Integrals · medium

The value of ∫0^π/2(sin x)/(sin x+cos x) dx is

Single correct option

The value of ∫0π/2sin⁡xsin⁡x+cos⁡x dx\displaystyle\int_0^{\pi/2}\frac{\sin x}{\sin x+\cos x}\,dx is
  1. A. π2\tfrac\pi2
  2. B. 11
  3. C. π4\tfrac\pi4
  4. D. π8\tfrac\pi8
Show answer and solution

Answer: (C) π4\tfrac\pi4

Let II be the integral. By the property ∫0af(x)dx=∫0af(a−x)dx\int_0^a f(x)dx=\int_0^a f(a-x)dx, also I=∫0π/2cos⁡xsin⁡x+cos⁡xdxI=\int_0^{\pi/2}\frac{\cos x}{\sin x+\cos x}dx. Adding gives 2I=∫0π/21 dx=π22I=\int_0^{\pi/2}1\,dx=\tfrac\pi2, so I=π4I=\tfrac\pi4.
Report a mistake

Original question written in the JEE Main 2016 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake