Question

Find the average value of f (x) = 1 / x on the interval [1, 3]. a) 1 / 3 b) 1 / 2 c) ln (3) d) 2 / 3

Answer 1

The average value of f(x) = 1/x on the interval [1, 3] is ln(3)/2.

Step-by-step explanation:

The average value of a function over an interval can be found by evaluating the definite integral of the function over that interval and dividing it by the length of the interval. In this case, f(x) = 1/x and the interval is [1, 3]. So, to find the average value, we need to evaluate the integral of 1/x over the interval [1, 3] and divide it by the length of the interval, which is 3 - 1 = 2.

Integrating 1/x gives ln|x|, so the average value of f(x) = 1/x on the interval [1, 3] is:

(ln(3) - ln(1))/2 = ln(3)/2