## 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 *b*−*a* 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.

## Related content in Oxford Index

##### Reference entries

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