定积分与积分和之间的误差讨论

Discussion on the Error between Finite In-tegral and Integral Sum

摘要: 本文主要讨论了定积分与其积分和由于点的取法及分割方法不同导致误差不同的一些问题，借用一元函数的几个中值公式进行推广探讨误差无穷小量的阶数，得到了定积分的点的取法不同及分割不同都可以导致误差的级别不同。

Abstract: This paper mainly discusses some problems about the difference between finite integral and its integral sum as well as the error caused by the difference of point selection and segmentation methods. In this paper, we discuss the order of infinitesimal of the error by making use of several Mean Value Theorems appeared in one-variable function, it is found that different points of definite integral and different division can lead to different error levels.