Putting Forward Another Generalization Of The Class Of Exponential Integrals And Their Applications.

Toyesh Prakash Sharma¹ , Etisha Sharma²

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.2 , pp.1-8, Apr-2023

Online published on Apr 30, 2023

Copyright © Toyesh Prakash Sharma, Etisha 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 :
The central aim of this paper is to introduce another generalization to the well-known integral from the class of exponential integrals. For a better understanding of the main result presented here. the knowledge of elementary integrations of continuous functions, definite and indefinite integration, the Concept of Mathematical Induction, and Basic Algebraic Manipulation are pre-requesting. Further on the basis of providing generalization, authors also give some applications that can show the generalization’s versatility, such as alternative proofs of the properties of Laplace Transform, Integration of e^ax sinbx and e^ax cosbx etc.

Key-Words / Index Term :
Elementary Integration, Definite Integral, Indefinite Integration, Exponential class of Integration, Upper and Lower Bounds, Laplace Transform, Integration by Parts etc.

References :
[1]. Toyesh Prakash Sharma, "A Generalization to? e x (ƒ (x) + ƒ1(x))dx", International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.6, pp.46-50, 2020.
[2]. Toyesh Prakash Sharma, "A Generalization to Integral e^-x. (f(x)-f’(x))dx", International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.1, pp.72-75, 2021.
[3]. NCERT- Mathematics Textbook for class XII Ch-7 integrals Ex-7.6. P.326. ISBN-81-7450-653-5.
[4]. Toyesh Prakash Sharma, "A Generalization to? e x (ƒ (x) + ƒ1(x))dx" section VI “Open Problem, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.6, pp.49, 2020.
[5]. Toyesh Prakash Sharma, "A Generalization to Integral e^-x. (f(x)-f’(x))dx" section IV “Open Problem”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.1, pp.75, 2021.
[6]. Toyesh Prakash Sharma, "Solution to an Open Problem", International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.4, pp.44-46, 2021.
[7]. Hj. Kim, “The intrinsic structure and properties of Laplace-typed integral transforms”, Mathematical Problem in Engineering, pp. 1-8, 2017.