一个推广的积分中值定理

A Generalized Mean Value Theorem for Integrals

积分中值定理是数学分析的基本定理,它在极限和积分的计算中有着广泛的应用.利用确界定义及介值定理,改进了混合积分中值定理.由该定理,可推导出可积函数具有介值性条件下的积分第一中值定理.

As a fundamental theorem of mathematics analysis, the mean value theorem for integrals is widely applied in calculation of limits and integrals. This paper, by using the definitions of supremum and infimum together with the intermediate value theorem, perfects the mixed mean value theorem for integrals. Based on this theorem, the first mean value theorem for integrable functions with the intermediate value property can be deduced.