定积分定义中的两个任意性  

Reducing Arbitrariness in the Definition of Definite Integral

作　　者：王烨 李雨生[2] 卜长江[1] WANG Ye;LI Yusheng;BU Changjiang(College of Mathematical Sciences,Harbin Engineering University,Harbin,Heilongjiang 150001,PRC;School of Mathematical Sciences,Tongji University,Shanghai 200092,PRC)

机构地区：[1]哈尔滨工程大学数学科学学院,黑龙江哈尔滨150001 [2]同济大学数学科学学院,上海200092

出　　处：《高等数学研究》2021年第6期9-11,25,共4页Studies in College Mathematics

基　　金：国家自然科学基金(11871377,11931002,12071097,12042103);黑龙江省高等教育教学改革项目(SJGY20180102);黑龙江省自然科学基金(LH2021A004).

摘　　要：在Riemann定积分的定义里,既有区间分割的任意性,又有小区间中取点的任意性.本文证明,定义中的任意性可以减少一个,或者分割为等分而保留小区间内取点的任意性,或者保留分割的任意性而小区间内取点全部为小区间右端点(或全部取为左端点),从而降低教学的难度.In the definition of the definite integral,the interval segmentations are arbitrary and the points in the sub-intervals are arbitrary.In this paper,we show that the arbitrariness can be reduced.We can either use the equal divisions and preserve the arbitrariness of the points in the sub-interval,or keep the arbitrariness of the interval segmentations but use in right endpoints of each sub-interval.

关 键 词：定积分定义 区间分割 小区间内取点 任意性 

分 类 号：O172[理学—数学]