Question

Find the average value of f(x) = sqrt(x² - 1)/x on the interval 1 ≤ x ≤ 7.

a) 1/2
b) 1/3
c) 1/4
d) 1/5

Answer 1

To find the average value of f(x) = sqrt(x² - 1) / x on the interval 1 ≤ x ≤ 7, use the Mean Value Theorem for Integrals and evaluate the definite integral of the function divided by the length of the interval.

Step-by-step explanation:

To find the average value of f(x) = sqrt(x² - 1) / x on the interval 1 ≤ x ≤ 7, we can use the Mean Value Theorem for Integrals.

The average value is equal to the definite integral of the function divided by the length of the interval. In this case, the average value is (1/6) * integral from 1 to 7 of sqrt(x² - 1) / x dx. You can evaluate the integral using techniques like substitution or integration by parts to get the final answer.