Find the average value of the function $f (x) = \frac{6}{x}$ on the interval $[1, 4]$ .
$f_{ave} =$

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Answer

$2 \log (4)$ is the average value of the function $f (x) = \frac{6}{x}$ on the interval $[1, 4]$ .

Steps

Step 1 ：Define the function $f (x) = \frac{6}{x}$ .

Step 2 ：Calculate the integral of the function $f (x) = \frac{6}{x}$ from 1 to 4, which is $6 \log (4)$ .

Step 3 ：Divide the integral by the length of the interval to find the average value, which is $2 \log (4)$ .

Step 4 ： $2 \log (4)$ is the average value of the function $f (x) = \frac{6}{x}$ on the interval $[1, 4]$ .