Two Methods of Proving the Improved Mean Value Theorem of Integral

DOI

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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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  - 10.2991/emcs-16.2016.132
ID  - Pei2016/01
ER  -