Overview

mean value


Show Summary Details

Quick Reference

(of a function)

Let f be a function that is continuous on the closed interval [a, b]. The mean value of f over the interval [a, b] is equal to

The mean value ȳ has the property that the area under the curve y=f(x) between x=a and x=b is equal to the area under the horizontal line y=ȳ between x=a and x=b, which is the area of a rectangle with width ba and height ȳ.

For example, the function may represent the temperature measured at a certain place over a period of 24 hours. The mean value gives what may be considered an ‘average’ value for the temperature over that period.

Subjects: Mathematics.


Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.