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Integral Calculus
Definite Integrals, Power Rule
jee_adv_2026_mock_p1
Grade 12

Question:

Match the following integrals in Column I with their values in Column II.

Step-by-Step Solution

Key Concept: Use the power rule of integration: ∫₀¹ x^n dx = 1/(n+1).
Step 1: P: ∫₀¹ x² dx = [x³/3]₀¹ = 1/3 => matches 1. Step 2: Q: ∫₀¹ x³ dx = [x⁴/4]₀¹ = 1/4 => matches 2. Step 3: R: ∫₀¹ x⁴ dx = [x⁵/5]₀¹ = 1/5 => matches 3. Step 4: S: ∫₀¹ x⁵ dx = [x⁶/6]₀¹ = 1/6 => matches 4.
Correct Answer: [P-1] [Q-2] [R-3] [S-4]
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