积分第一中值定理的改进

Improvement of the First Integral Mean Value Theorem

积分第一中值定理是高等数学课程中的基本定理之一,有着广泛的应用价值.从教材积分第一中值定理入手,对积分第一中值定理加以改进,减弱其条件而加强其结论,给出积分第一中值定理的其它形式,并对此定理加以推广.

The First Integral Mean Value Theorem is one of the basic theorems of advanced mathematics,which has widespread application.This paper begins with the statement in the text book.This article tries to improve the First Integral Mean Value Theorem and weaken its conditions while strengthening its conclusion.It shows other forms of the First Integral Mean Value Theorem and extends the theory finally.