The value of ∫[0 to π/2] (sin x)/(sin x + cos x) dx is:
Correct: B
Let I = ∫[0 to π/2] (sin x)/(sin x + cos x) dx. Use the property ∫[0 to a] f(x) dx = ∫[0 to a] f(a-x) dx. Therefore, I = ∫[0 to π/2] (sin(π/2 - x))/(sin(π/2 - x) + cos(π/2 - x)) dx = ∫[0 to π/2] (cos x)/(cos x + sin x) dx. Adding the two expressions for I, we get 2I = ∫[0 to π/2] (sin x + cos x)/(sin x + cos x) dx = ∫[0 to π/2] 1 dx = [x][0 to π/2] = π/2. Therefore, I = π/4.