Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 10, 17 November 2023
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Lobachevsky's formula and its applications to several definite integrals
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Abstract
The definite integral is a fundamental concept in calculus that has many applications in various fields such as physics, engineering, and economics. However, integration can be difficult and requires a variety of skills such as substitutions and partial integration. In this paper, Lobachevsky’s formula is explored, which provides a new way to evaluate definite integrals. It should be noted that Lobachevsky’s formula can only be applied in specific cases where the integrand is even and π-periodic. However, it is demonstrated to be an effective method in these cases. In this paper, the proof of the theorem is given, and a variety of examples are solved by virtue of this method. Hence, this paper may serve as a reference for relevant research in the field of calculus and provide insights into the applications of Lobachevsky’s formula.
Keywords
Lobachevsky's formula, definite integral, improper integral, calculus
References
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Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 2023 International Conference on Mathematical Physics and Computational Simulation
- ISBN (Print)
- 978-1-83558-131-5
- ISBN (Online)
- 978-1-83558-132-2
- Published Date
- 17 November 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/10/20230324
- Copyright
- 17 November 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited