Integral Calculus
Definite Integrals, Average Value
jee_main_2026_april_4_shift_2
Grade 12
Question:
If ∫_1^2 (2x + 3) dx = a, and the average value of f(x) = 2x + 3 on [1, 2] is b, find a - b.
Step-by-Step Solution
Key Concept: Evaluate integral for a; average value = (1/(b-a))∫_a^b f(x) dx.
Step 1: a = ∫_1^2 (2x+3) dx = [x^2 + 3x]_1^2 = (4+6) - (1+3) = 10 - 4 = 6. Step 2: b = (1/(2-1))∫_1^2 (2x+3) dx = 6. Step 3: a - b = 6 - 6 = 0.
Correct Answer: 0
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