Integral Calculus
Definite Integrals, Power Rule
jee_main_2026_april_6_shift_2
Grade None
Question:
If ∫_0^1 (x² + 2) dx = a, and ∫_0^1 (2x + 1) dx = b, find a - b.
A. 1/3
B. 2/3
C. 1
D. 4/3
Step-by-Step Solution
Key Concept: Evaluate both definite integrals using power rule.
Step 1: a = [x³/3 + 2x]_0^1 = 1/3 + 2 = 7/3. Step 2: b = [x² + x]_0^1 = 1 + 1 = 2. Step 3: a - b = 7/3 - 2 = 7/3 - 6/3 = 1/3.
Correct Answer: A
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