Question

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

Answer 1

(1+e)/2

Answer 2

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

Answer 3

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