Integral Calculus
Definite Integrals, Integration Techniques
jee_adv_2026_mock_p2
Grade 12
Question:
If ∫_0^1 (x^3)/(1 + x^2) dx = a - (1/2) ln 2, find the value of 2a.
Step-by-Step Solution
Key Concept: Use polynomial division: x^3/(1+x^2) = x - x/(1+x^2).
Step 1: ∫_0^1 x^3/(1+x^2) dx = ∫_0^1 (x - x/(1+x^2)) dx. Step 2: = [x^2/2 - (1/2) ln(1+x^2)]_0^1 = 1/2 - (1/2) ln 2. Step 3: So a = 1/2, 2a = 1.
Correct Answer: 1
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