Approximating Non-Elementary Integrals Appling Elementary Techniques Of Integration And Inequalities.

Toyesh Prakash Sharma¹ , Ankush Kumar Parcha²

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.2 , pp.17-26, Apr-2023

Online published on Apr 30, 2023

Copyright © Toyesh Prakash Sharma, Ankush Kumar Parcha . 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 :
The central aim of this paper is to put forward an aspect of functional inequality for finding nearby numerical values of non-elementary integrals without using advanced calculus and advanced functions like the Gamma function Incomplete gamma function, Beta function, Error function etc.. Still, for matching the values of those non-elementary integrals for some fixed lower and upper bounds of it there we use Wolfram Alpha and Desmos. For a better understanding, readers should be aware of Cauchy-Bunyakovsky-Schwarz Integral Inequality, Hermite-Hadamard Inequality for Convex functions, Hermite-Hadamard Inequality for Concave functions etc.

Key-Words / Index Term :
Elementary Integrals, non-elementary Integrals, Closed Form, Upper Bound and Lower Bound, Error Functions, Convex Functions, Concave Function, Strictly Increasing Function, Cauchy-Bunyakovsky-Schwarz Integral Inequality, Hermite-Hadamard Inequality for Convex and Concave functions, Hermite-Hadamard Inequality for Concave functions etc.

References :
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[6] G.H. Hardy, Littlewood, G. Pólya,” Inequalities.” Cambridge University Press, Cambridge pp.324, 1952.
[7] Toyesh Prakash Sharma, "Application of Inequalities for Finding Range of Non-elementary Integrals," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.5, pp.8, 2022.

[8] Toyesh Prakash Sharma, "Application of Inequalities for Finding Range of Non-elementary Integrals," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.5, pp.13, 2022.
[9] Toyesh Prakash Sharma, "Application of Inequalities for Finding Range of Non-elementary Integrals," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.5, pp.15, 2022.