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Integral Calculus

Definite Integrals, Properties

jee_main_2026_april_2_shift_1

Grade 12

Question:

The value of ∫_0^(π/2) (sin x)/(sin x + cos x) dx is:

A. 0

B. 1/2

C. π/4

D. π/2

Step-by-Step Solution

Key Concept: Use the property ∫_0^a f(x) dx = ∫_0^a f(a-x) dx.

Step 1: Let I = ∫_0^(π/2) sin x/(sin x + cos x) dx. Step 2: Using property, I = ∫_0^(π/2) cos x/(sin x + cos x) dx. Step 3: Adding: 2I = ∫_0^(π/2) 1 dx = π/2. Step 4: Therefore, I = π/4.

Correct Answer: C

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