Calculus problem

Question

Find the average value of the function f(x)=(9/sqrt x) on [2,8]

Answer 1

First of all, when we graph the function we see it looks like this:

So we can see that the values range from 3.2 to 6.4 so the AVERAGE value should be in the 4 1/2 range or so.

To find the average in general, we add up all the numbers and divide by the number of numbers. In this case, to add up all the numbers, we need to integrate then divide by the difference in the x values.so:

average value = ₂∫⁸f(x)dx /(8-2) = 25.4558/6 = 4.243