Proceedings of the 2016 International Conference on Education, Management, Computer and Society

Two Methods of Proving the Improved Mean Value Theorem of Integral

Authors
Hongmei Pei, Xuanhai Li, Jielin Shang
Corresponding Author
Hongmei Pei
Available Online January 2016.
DOI
https://doi.org/10.2991/emcs-16.2016.132How to use a DOI?
Keywords
Mean value theorem of integral; Mean value theorem of differential; Improved; Maximum and minimum value; Comparison Property
Abstract

The proof of the mean value theorem for integral, which is given by Advanced Mathematics and which is wildly used, only proved that the mean value is on the closed interval. In this paper, we provide two different methods for the proof of the mean value theorem of integral and prove the mean value is in the open interval, which is an improvement in the conclusion of the theorem. In the end, we illuminates the practicability of the improved mean value theorem for integral with two examples as follows.

Copyright
© 2016, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 2016 International Conference on Education, Management, Computer and Society
Series
Advances in Computer Science Research
Publication Date
January 2016
ISBN
978-94-6252-158-2
ISSN
2352-538X
DOI
https://doi.org/10.2991/emcs-16.2016.132How to use a DOI?
Copyright
© 2016, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Hongmei Pei
AU  - Xuanhai Li
AU  - Jielin Shang
PY  - 2016/01
DA  - 2016/01
TI  - Two Methods of Proving the Improved Mean Value Theorem of Integral
BT  - Proceedings of the 2016 International Conference on Education, Management, Computer and Society
PB  - Atlantis Press
SP  - 546
EP  - 550
SN  - 2352-538X
UR  - https://doi.org/10.2991/emcs-16.2016.132
DO  - https://doi.org/10.2991/emcs-16.2016.132
ID  - Pei2016/01
ER  -