Definition:Average Value of a Function
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Definition
Let $f$ be an integrable function on some closed interval $\left[{a..b}\right]$.
The average value of $f$ (or mean value of $f$) on the interval is defined as:
- $\displaystyle \frac 1 {b-a}\int_a^b f \left({x}\right) \ \mathrm d x$
Also see
- Mean Value Theorem for Integrals which proves that such a number exists.
Note on Terminology
The word average is generally considered to be too vague for use in mathematics, as it could mean one of a number of kinds of average.
For serious mathematics it is considered preferable to use the term mean value rather than average value.
However, this is a significant elementary concept which has applications across a wide range of applied mathematics and soft-science subjects, and the popular terminology in such circumstances takes precedence.
