Difference Quotient Formula

Given that the mean value, derivative expression form provides all of the same information as the classical integral notation, the mean value form may be the preferable expression, such as in writing venues that only support/accept standard ASCII text, or in cases that only require the average derivative (such as when finding the average radius in an elliptic integral).
This is especially true for definite integrals that technically have (e. g. ) 0 and either π{displaystyle pi ,!} or 2π{displaystyle 2pi ,!} as boundaries, with the same divided difference found as that with boundaries of 0 and π2{displaystyle {begin{matrix}{frac {pi }{2}}end{matrix}}} (thus requiring less averaging effort):

a b c d e f g h i j k l m n o p q r s t u v w x y z