Calculation of definite integrals using probability distributions
DOI:
https://doi.org/10.35819/remat2021v7i1id4694Keywords:
Probability Distributions, Definite Integrals, Calculation, ProbabilityAbstract
This article is a part of a monograph of one of the authors and is directed to those interested in concepts from the subjects of Integral Calculus and Probability. In this sense, it is proposed an alternative technique for solving definite integrals and until then not presented in the literature, according to the research carried out. For the development of this article, the probability distribution functions of the Beta and Exponential distributions, their properties and the Fundamental Theorem of Calculus will be emphasized as theoretical support to the reader. Subsequently, two definite integrals are solved to exemplify the proposed technique, followed by the generalization of the functions that can be integrated through the Exponential and Beta distributions. It is possible to show that the proposed method, in addition to being an alternative procedure for the resolution of definite integrals, offers the advantage of reducing the necessary calculations when using the integration techniques proposed in the Integral Calculus literature.
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References
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MORETTIN, L. G. Estatística Básica. São Paulo: Pearson Prentice Hall, 2010.
SANTOS, D. S. N. Cálculo de integrais definidas utilizando funções de distribuição de probabilidade. Orientadora: Fernanda Vital de Paula. 2014. 35f. Monografia (Graduação em Matemática) - Universidade Federal do Tocantins, Araguaína, 2014.
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https://orcid.org/0000-0002-0893-7426
