Two Methods of Proving the Improved Mean Value Theorem of Integral
- https://doi.org/10.2991/emcs-16.2016.132How to use a DOI?
- Mean value theorem of integral; Mean value theorem of differential; Improved; Maximum and minimum value; Comparison Property
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.
- © 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 -