摘要
在确定被积函数单调性的情况下继续研究第二积分中值定理中值点存在唯n(n=1,2,3,…)或充满一个区间的充要条件.在此基础上,又继续研究多中值点当x趋于端点和无穷时的渐近性态,所得结果改进和推广了所列文献的若干结果;最后应用Mathematica数学软件对以上理论结果给出了可视化实例验证.
In this paper,in the case of the integrand increases or decreases,the necessary and sufficient conditions for the existence of exact n(n=1,2,.)or suffusing an interval of the mean value points are studied.Then the asymptotic behavior of multiple mean value points are discussed and some more generalized conclusions to improve some results of references are drawn.Finally,by using mathematical software,Mathematica,the visualization of the theoretical results are given.
作者
仉志余
苗雨
ZHANG Zhi-yu;MIAO Yu(Department of Science,Taiyuan Institute of Technology,Taiyuan 030008,China;School of Mathematical Sciences,Capital Normal University,Beijing 100048,China)
出处
《数学的实践与认识》
2023年第7期278-288,共11页
Mathematics in Practice and Theory
基金
国家自然科学基金(11701528)
山西省自然科学基金(2011011002-3)。
关键词
第二积分中值定理
积分中值点
渐近性
可视化
second integral mean value theorem
mean value point for integral
asymptotic behavior
visualization
