What is the average value of the function f(x) = 6x on the closed interval [1, 4]?
Answer and explanation
Correct answer: B. 15
- Step 1: The average value formula is f_avg = (1 / (b - a)) * integral from a to b of f(x) dx.
- Step 2: Here, b - a = 4 - 1 = 3.
- Step 3: Evaluate the integral: integral from 1 to 4 of 6x dx = [3x^2] from 1 to 4 = 3(16) - 3(1) = 48 - 3 = 45.
- Step 4: Divide by interval length: 45 / 3 = 15.
Answer
15.
Why not the others: '18' averages f(1)=6 and f(4)=24 incorrectly without integration; '30' omits dividing by (b - a); '12' computes 6 * (4 - 1) - 6.
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