Integral Calculus
Definite Integrals, Properties
jee_main_2026_jan_21_shift_1
Grade None
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: I = ∫₀^{π/2} cos x/(sin x + cos x) dx. Step 3: 2I = ∫₀^{π/2} 1 dx = π/2. Step 4: I = π/4.
Correct Answer: C
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