Question

What is the average value of the function `f(x)=2/x` on the interval `[1,10]`?

Answer 1

`= 2/9 ln(10)`

Explanation:

`f(x)=2/x`

By definition:
`f_{ave} = (\int_a^b \ f(x) \ dx)/(b-a)`

here we have
`f_{ave} = (\int_1^{10} \ 2/x \ dx)/(10-1)`

`= ( [ 2ln(x) ]_1^{10})/9`

`= 2/9 ln(10)`