Find the exact average value?

Question

Fine the exact average value of f(x) = 1/(x+1) on the interval x=0 and x=2.

Answer 1

The average value is:

int(0, 2) [ f(x) ] dx / (2 - 0)

= ln(x + 1) ] (0, 2) / 2

= [ ln(3) - ln(1) ] / 2

= ln(3) / 2.