Definition:Average Value of Function

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Let $f$ be an integrable function on some closed interval $\closedint a b$.

The average value of $f$ (or mean value of $f$) on $\closedint a b$ is defined as:

$\ds \frac 1 {b - a} \int_a^b \map f x \rd x$

Also see

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.