Determine the average value of the function f(x) = √x on 1 ≤ x ≤ 36.

Answer 1

You need to be clear what it is that you want.

For some applications the average value of a function f over an interval is the integral of f over the interval divided by the length of the interval.

The "mean" of a distribution function (for which the integral over the interval is 1), is the integral of xf(x) over the interval.

Just a little further help the integral of x^1/2 is (2/3)x^3/2.