Integral Calculus
Definite Integrals, Trigonometric Integration
jee_main_2026_april_4_shift_1
Grade 12
Question:
The value of ∫_0^(π/4) (tan x)/(1 + tan^2 x) dx is:
A. 1/4
B. 1/2
C. 1/3
D. 1/6
Step-by-Step Solution
Key Concept: 1 + tan^2 x = sec^2 x, so the integral simplifies to ∫ sin x cos x dx.
Step 1: ∫_0^(π/4) tan x/(sec^2 x) dx = ∫_0^(π/4) sin x cos x dx. Step 2: = [sin^2 x/2]_0^(π/4) = 1/2(1/2 - 0) = 1/4.
Correct Answer: A
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