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Integral Calculus

Definite Integrals, Power Rule

jee_main_2026_april_5_shift_1

Grade 12

Question:

If ∫_0^1 (3x² + 2x) dx = a, and ∫_0^1 (4x³ + 3x²) dx = b, find a + b.

A. 1

B. 2

C. 3

D. 4

Step-by-Step Solution

Key Concept: Evaluate both definite integrals using power rule.

Step 1: a = [x³ + x²]_0^1 = 1 + 1 = 2. Step 2: b = [x⁴ + x³]_0^1 = 1 + 1 = 2. Step 3: a + b = 4.

Correct Answer: D

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