Using the property of definite integrals, evaluate ∫[0 to π/2] (sin x)/(sin x + cos x) dx.

Using the property of definite integrals, evaluate ∫[0 to π/2] (sin x)/(sin x + cos x) dx.

• A. π/2
• B. π
• C. 0
• D. π/4

Answer: D) π/4

Explanation: Let I = ∫[0 to π/2] (sin x)/(sin x + cos x) dx. Using property ∫[0 to a] f(x) dx = ∫[0 to a] f(a-x) dx, I = ∫[0 to π/2] (cos x)/(cos x + sin x) dx. Adding both gives 2I = ∫[0 to π/2] 1 dx = π/2. So, I = π/4.