Definition of Average in the Integral Sense.md

The formula for the average value of a function ($f(x)$) over an interval $[a, b]$ is given by: $$ \overline{f} = \frac{1}{b - a} \int_{a}^{b} f(x) , dx $$

In this formula:

• $a$ and $b$ are the lower and upper bounds of the interval over which you want to find the average of $f(x)$.
• $f(x)$ is the function whose average you want to calculate.
• $\int_{a}^{b} f(x) , dx$ represents the definite integral of $f(x)$ over the interval $[a, b]$.
• $\frac{1}{b - a}$ scales the integral result to find the average value over the interval.

This formula essentially calculates the mean value of the function $f(x)$ over the specified interval.