Find the average value of f(x) = 1 over x over the interval [e, 2e]

Question

Find the average value of f(x) =  over the interval [e, 2e].

 

  

Ln2 

Ln3

Answer 1

Ave = ∫_a^b f(x) dx/(b-a) = ∫_e^2e 1/x dx /(2e-e) = ln(x)|_e^2e /e = (ln(2e)-ln(e))/e = (ln(2)+1-1)/e = ln(2)/e

note: ln(e) = 1 and ln(2e) = ln(2)+ln(e)