Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 31, 07 March 2024
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Comparative study of riemann integral and lebesgue integral in calculus
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Abstract
The aim of this research paper is to provide a comprehensive comparison between Riemann integral and Lebesgue integral. Integration is described as the inverse process of differentiation, which is used to determine the original function. Riemann integration is a specific type of definite integral applied to find the exact area under a function graph between two limits in a closed interval. Lebesgue integration, on the other hand, provides a more generalized framework for integration theory. Integrals are essential in mathematical modelling and analysis tools. Studying and comparing the similarities and differences between these two integration methods can help us better understand the essence and properties of integrals, so as to more accurately apply integration methods to solve practical problems. This paper provides a systematic analysis of the basics, definitions, concepts, and properties of Riemann integral and Lebesgue integral. Reasoning, proofs, and examples are consolidated to explain the properties and characteristics of these two integral methods. Finally, this paper explores the strengths and limitations of each integration methods, summarising their advantages and applicability to practical problems and providing insights into their respective computational methods and applicability in different contexts.
Keywords
Riemann integral, Lebesgue integral, comparison
References
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5. Pang X C, et al. 2019 Mathematical Analysis. Higher Education Press, 186-187.
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8. Zhang Y L, et al. 2020 The relationship of Lebesgue Integral and Riemann Integral. Journal of Jiaozuo Teachers College Mar, 70-76.
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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 3rd International Conference on Computing Innovation and Applied Physics
- ISBN (Print)
- 978-1-83558-317-3
- ISBN (Online)
- 978-1-83558-318-0
- Published Date
- 07 March 2024
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/31/20240731
- Copyright
- 07 March 2024
- 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