## anonymous 5 years ago the average (mean) value of 1/x over the interval 1 less than or equal to x less than or equal to "e" is?

1. anonymous

(1+e)/2

2. anonymous

The average of a function $$f(x)$$ in a given interval is $$[a,b]$$ is given by $$\frac{1}{b-a} \int_a^b f(x)dx$$.

3. anonymous

In this case the average is $$\frac{1}{e-1} \int_1^e \frac{dx}{x}=\frac{1}{e-1} (\ln e-\ln 1)=\frac{1}{e-1}.$$