example of integral mean value theorem


If f is a continuousMathworldPlanetmath real function on an interval [a,b], then there exists a ζ(a,b) such that


Let g(x)1. Then by the Integral Mean Value Theorem, there exists ζ(a,b) such that

abf(x)dx =abf(x)g(x)dx

as required. ∎

Title example of integral mean value theorem
Canonical name ExampleOfIntegralMeanValueTheorem
Date of creation 2013-03-22 18:20:24
Last modified on 2013-03-22 18:20:24
Owner me_and (17092)
Last modified by me_and (17092)
Numerical id 4
Author me_and (17092)
Entry type Example
Classification msc 26A06