在线积分计算器与不定积分的概念

IF 0.7 Q3 EDUCATION & EDUCATIONAL RESEARCH

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-04-21 DOI:10.1080/0020739X.2022.2047810

E. M. Vorob’ev

{"title":"在线积分计算器与不定积分的概念","authors":"E. M. Vorob’ev","doi":"10.1080/0020739X.2022.2047810","DOIUrl":null,"url":null,"abstract":"This paper discusses the mathematical and didactical problems of teaching indefinite integral in the context of the ubiquitous availability of online integral calculators. The symbol of indefinite integral introduced by Leibniz, unfortunately, does not contain an indication of the interval on which the antiderivatives should be calculated. This yields mismatched results of calculating the same integral on different online calculators. The paper justifies the expediency of including the interval of integration in the designation of indefinite integral or, at least, in the settings of problems of its calculation. Indication of the integration interval ensures the uniqueness of the solution to the problem of calculating the indefinite integral, the uniqueness that does not occur in the traditional setting of the integration problem. This is important because online calculators provide users with formulas that differ from each other and can represent both different and coincidental antiderivatives of the same function. Analysis of the domains of definition of the obtained by calculators antiderivatives allows users to understand how they relate to each other.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"54 1","pages":"630 - 637"},"PeriodicalIF":0.7000,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Online integral calculators and the concept of indefinite integral\",\"authors\":\"E. M. Vorob’ev\",\"doi\":\"10.1080/0020739X.2022.2047810\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper discusses the mathematical and didactical problems of teaching indefinite integral in the context of the ubiquitous availability of online integral calculators. The symbol of indefinite integral introduced by Leibniz, unfortunately, does not contain an indication of the interval on which the antiderivatives should be calculated. This yields mismatched results of calculating the same integral on different online calculators. The paper justifies the expediency of including the interval of integration in the designation of indefinite integral or, at least, in the settings of problems of its calculation. Indication of the integration interval ensures the uniqueness of the solution to the problem of calculating the indefinite integral, the uniqueness that does not occur in the traditional setting of the integration problem. This is important because online calculators provide users with formulas that differ from each other and can represent both different and coincidental antiderivatives of the same function. Analysis of the domains of definition of the obtained by calculators antiderivatives allows users to understand how they relate to each other.\",\"PeriodicalId\":14026,\"journal\":{\"name\":\"International Journal of Mathematical Education in Science and Technology\",\"volume\":\"54 1\",\"pages\":\"630 - 637\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-04-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Mathematical Education in Science and Technology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/0020739X.2022.2047810\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"EDUCATION & EDUCATIONAL RESEARCH\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mathematical Education in Science and Technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/0020739X.2022.2047810","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}

引用次数: 0

摘要

本文讨论了在在线积分计算器普遍可用的背景下，不定积分教学的数学和教学问题。不幸的是，莱布尼茨引入的不定积分符号没有包含反导数应该在其上计算的区间的指示。这会产生在不同的在线计算器上计算相同积分的不匹配结果。本文证明了在不定积分的指定中，或者至少在其计算问题的设置中，包括积分区间的方便性。积分区间的指示确保了计算不定积分问题的解的唯一性，这种唯一性在积分问题的传统设置中不会出现。这一点很重要，因为在线计算器为用户提供了彼此不同的公式，并且可以表示同一函数的不同和巧合的反导数。通过分析计算器获得的反导数的定义域，用户可以了解它们之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Online integral calculators and the concept of indefinite integral

This paper discusses the mathematical and didactical problems of teaching indefinite integral in the context of the ubiquitous availability of online integral calculators. The symbol of indefinite integral introduced by Leibniz, unfortunately, does not contain an indication of the interval on which the antiderivatives should be calculated. This yields mismatched results of calculating the same integral on different online calculators. The paper justifies the expediency of including the interval of integration in the designation of indefinite integral or, at least, in the settings of problems of its calculation. Indication of the integration interval ensures the uniqueness of the solution to the problem of calculating the indefinite integral, the uniqueness that does not occur in the traditional setting of the integration problem. This is important because online calculators provide users with formulas that differ from each other and can represent both different and coincidental antiderivatives of the same function. Analysis of the domains of definition of the obtained by calculators antiderivatives allows users to understand how they relate to each other.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

International Journal of Mathematical Education in Science and Technology EDUCATION & EDUCATIONAL RESEARCH-

CiteScore

3.30

自引率

11.10%

发文量

123

期刊介绍： Mathematics is pervading every study and technique in our modern world, bringing ever more sharply into focus the responsibilities laid upon those whose task it is to teach it. Most prominent among these is the difficulty of presenting an interdisciplinary approach so that one professional group may benefit from the experience of others. The International Journal of Mathematical Education in Science and Technology provides a medium by which a wide range of experience in mathematical education can be presented, assimilated and eventually adapted to everyday needs in schools, colleges, polytechnics, universities, industry and commerce. Contributions will be welcomed from lecturers, teachers and users of mathematics at all levels on the contents of syllabuses and methods of presentation.