Question

How do you find the average value of the function `f(x) = 12/(sqrt(2x-1))` on the interval of [1,5]?

Answer 1

Have a look:

Answer 2

The idea for positive functions:
The average value is the height of a horizontal line that gives a rectangle on the interval whose area is equal to the area under the curve.

Average value of `f(x)` on `[a,b]` is

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

So find
`int_1^5 12/sqrt(2x-1) dx` (By substitution.)

`= 12 sqrt(2x-1)]_1^5`

`=12(3) - 12(1) = 24`

Now divide by the length of the interval:

`24/(5-1) = 24/4 = 6`

The average value is `6`