# How do you find the average value of the function for f(x)=1/x, 1<=x<=4?

Apr 10, 2017

$\ln \sqrt[3]{4} \approx 0.462$

#### Explanation:

The $\textcolor{b l u e}{\text{average value}}$ is.

$\frac{1}{b - a} {\int}_{a}^{b} f \left(x\right) \mathrm{dx}$

$= \frac{1}{4 - 1} {\int}_{1}^{4} \left(\frac{1}{x}\right) \mathrm{dx}$

$= \frac{1}{3} {\left[\ln x\right]}_{1}^{4}$

$= \frac{1}{3} \left[\ln 4 - \ln 1\right]$

$= \ln \sqrt[3]{4} \approx 0.462 \text{ to 3 dec. places}$