Application of Inequalities for Finding Range of Non-elementary Integrals

Toyesh Prakash Sharma¹

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.5 , pp.7-20, Oct-2022

Online published on Oct 31, 2022

Copyright © Toyesh Prakash Sharma . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This paper aims to use inequalities and functional inequality for approximating non-elementary integrals or finding nearby numerical values of non-elementary integrals without using advanced calculus and advanced functions like the error function, Incomplete gamma function, but for matching the values of those non-elementary integrals for some fixed lower and upper bound of it there we use Wolfram Alpha. for the better understanding reader should be aware of Cauchy-Schwarz Integral Inequality, Hermite-Hadamard Inequality for Convex functions, Hermite-Hadamard Inequality for Concave functions, Jensen`s Inequality for Concave and Convex function, Generalized Arithmetic-Geometric Mean Inequality etc.

Key-Words / Index Term :
Elementary Integrals, non-elementary Inegrals, Closed Form, Upeer Bound and Lower Bound etc.

References :
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