关于广义积分中值定理及“中间点”的渐近性

On the Mean Value Theorem for Improper Integral and the Asymptotic Property of the “Intermediate Point”

首先建立了无界函数广义积分的各种中值定理，并系统地讨论了其“中间点”的渐近性，得到一系列结果，推广了有关文献中关于定积分的一些结论，然后，由此导出了无穷限积分的相应性质。

This paper first sets up each class mean value theorems for improper integral of unbounded function, and systemally discusses the asymptotic properties of their“intermediate point”, the paper obtains a series of results, and extends some conclusions of definite integral in some references, then infers corresponding properties of infinite integral by these results.