Different approaches to calculate real integrals
DOI:
https://doi.org/10.22481/intermaths.v2i2.9487Keywords:
Teorema dos Resíduos, Lema de Jordan, Funções Analíticas, Integrais ReaisAbstract
We present three distinct ways to approach a real integral, a class of integrals, since the integral depends on two parameters. The first way uses a general result, a theorem; the second way, complex variables, through of the residue theorem and Jordan's lemma, while the third way, an artifice through real functions, without using the complex plane. The goal is to make the student choose the best way to approach this class of integrals, or possibly, propose another different way.
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Vaz Jr, J. e De Oliveira, E. C. Métodos Matemáticos, Volume 1, 1ªed. Campinas: Editora da Unicamp, 2016.
De Oliveira, E. C. e Rodrigues Jr., W. A. Funções Analíticas com Aplicações, 1ªed. São Paulo: Editora Livraria da Física, 2005.
Churchill, R. V. Variáveis Complexas e suas Aplicações, 1ªed. São Paulo: Editora da Universidade de São Paulo-Editora McGraw-Hill do Brasil, 1975.
Ablowitz, M. J. and Fokas, A. S. Complex Variables: Introduction and Applications, in Cambridge Texts in Applied Mathematics, 1 st ed. Cambridge: Cambridge University Press, 1999.
Vaz Jr, J. e De Oliveira, E. C. Métodos Matemáticos, Volume 2, 1ªed. Campinas: Editora da Unicamp, 2016.
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