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《Studies in College Mathematics》 2012-06
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On the Addition of Indefinite Integrals

ZHOU Qin (School of Mathematical Sciences,University of Jinan,Jinan 250022,PRC)  
In view of the phenomenon of lacking accurate definition and reasonable explanation about the operations of indefinite integrals,this paper takes "+" operation between indefinite integrals as an example to construct a quotient group(C(I)/R;),the set of equivalent classes \R,which is conventionally the indefinite integral ∫f(x)dx if F′(x)=f(x).This reveals that the binary operation"" in the equivalent class(C(I)/R;) is the essence of "+" operation between indefinite integrals.
【Fund】: 山东省教育厅基础学科建设专项基金(JCXK0606)
【CateGory Index】: O172.2
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【Citations】
Chinese Journal Full-text Database 4 Hits
1 ZHOU Qin (School of Science,University of Jinan,Jinan 250022,China);A More Precise Statement of the Definition of Indefinite Integral[J];College Mathematics;2010-04
2 ZHANG Li (Hunan Vocational College of Commerce, Changsha Hunan 410205, China);The issues on the definition and calculation of Indefinite Integral[J];Journal of Hunan University of Science and Engineering;2008-08
3 Mo Shaokui(Department of Mathematics, Nanjing University, 210008, Nanjing, PRC);NEW TREATMENT OF INDEFINITE INTEGRALS[J];JOURNAL OF NAIJING UNIVERSITY (NATURAL SCIENCES);1994-02
4 ZHANG Zhou-ping~1,JIAO Zhan-ya~1,HU Yu-pu~2(1.College of Computer and Information Engineering, Shaanxi University of Science & Technology, Xianyang 712081,China;2.College of Telecommunication Engineering, Xidian University, Xi′an 710071,China);CONGRUENCE RELATION AND QUOTIENT GROUP[J];Journal of Shaanxi University of Science & Technology;2004-06
【Co-citations】
Chinese Journal Full-text Database 6 Hits
1 LIU Jing,GUO Ji-dong(Mathematics Department,Ili Normal University,Yining 835000,China);Discussion to Part Properties of Rough Group and Quotient Group[J];Journal of Baicheng Normal College;2008-03
2 ZHOU Qin (School of Science,University of Jinan,Jinan 250022,China);A More Precise Statement of the Definition of Indefinite Integral[J];College Mathematics;2010-04
3 HU Hong-chi1,WEI Ning2(1.Department of Mathematics,Tangshan Normal College,Tangshan 063000,China;2.Department of Foundation,Hebei Energy Institute of Vocation and Technology,Tangshan 063000,China);The demonstration of equivalence between two infinite integral convegence[J];Journal of Science of Teachers' College and University;2007-06
4 Liu Yongjian(Department of Mathematics and Computation Science,Yulin Normal University,Yulin Guangxi 537000,P.R.China);Discussion about the Teaching of Extreme Value of Function[J];China Education Innovation Herald;2011-17
5 ZHOU Qin (School of Science,University of Jinan,Jinan 250022,China);Indefinite Integral and Quotient Group[J];Journal of University of Jinan(Science and Technology);2009-03
6 ZHANG Hui;School of Science, Shaanxi University of Science and Technology;;A Study of the Mathematical Humanistic Approach to the Teaching of Advanced Mathematics[J];Journal of Xianyang Normal University;2014-06
【Secondary Citations】
Chinese Journal Full-text Database 4 Hits
1 TANG Xiao-dan (Guizhou University for Ethnic Minorities,Guiyang,Guizhou 550025,China);An analysis and counter-measures on some common mistakes of indefinite integral[J];Journal of Guizhou Educational College;2004-02
2 Mo Shaokui(Department of Mathematics, Nanjing University, 210008, Nanjing, PRC);NEW TREATMENT OF INDEFINITE INTEGRALS[J];JOURNAL OF NAIJING UNIVERSITY (NATURAL SCIENCES);1994-02
3 ZHOU Qin (School of Science,University of Jinan,Jinan 250022,China);Indefinite Integral and Quotient Group[J];Journal of University of Jinan(Science and Technology);2009-03
4 DENG Le-bin(Maths Department,Yunyang Teachers College,Danjiangkou 442700,China);Analysis on Common Mistakes in Integral Calculation[J];Journal of Yunyang Teachers College;2006-03
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