Question

How do you find the average value of `f(x)=sqrtx` as x varies between `[0,4]`?

Answer 1

The average value of `f(x)=sqrt(x)` as `x in [0,4]` is `4/3`

Explanation:

The integral average of`f(x)` over the interval `(a,b)` is calculated as:

`bar f = 1/(b-a) int_a^b f(x)dx`

In our case:

`bar f = 1/4int_0^4 sqrt(x)dx = 1/4[2/3x^(3/2)]_0^4=1/6 (4*sqrt(4))=4/3`