Hi hows it going

In the Fundamental Theorem of Calculus;

$\displaystyle \Delta F \ = \ F(b) \ - \ F(a) \ and \ \Delta x \ = \ b \ - \ a $

we can rewrite this as;

$\displaystyle \Delta F \ = \ \int_{a}^{b} f (x)\,dx$

Then if we multiply both sides by 1/Δx we get;

$\displaystyle \frac{\Delta F}{ \Delta x} \ = \ \frac{1}{b \ - \ a} \int_{a}^{b} f (x)\,dx $

This is called the Average of the function f.

What does this mean?

I was always extremely bad at any form of statistics because I didn't understand it but maybe now I'll get it. Would this be like those graphs of average rainfall throughout the year where they showed the 12 months and the rainfall in each month and you had to find the average for the year?

It just makes very little sense to me and I don't know what it's good for. When would this be useful to implement?