Integration method of non-elementary exponential functions using iterated Fubinni integrals

Authors

DOI:

https://doi.org/10.31686/ijier.vol9.iss9.3326

Keywords:

Non-elementary exponential functions, Approaches, Integrals, Taylor series

Abstract

The present work presents a new method of integration of non-elementary exponential functions where Fubinni's iterated integrals were used. In this research, some approximations were used in order to generalize the results obtained through mathematical series, in addition to integration methods and double integrals. In addition to the integration methods, the Taylor series was used, where the value found and compatible with the values ​​of the power series that are used to calculate the value of the exponential function demonstrated in the work was verified. In addition to the methods described, a comparison of the values ​​obtained by the series and the values ​​described in the method was improvised, where it was noticed that the higher the value of the variable, the closer the results show a stability for the variable greater than the value 4, described in table 01. The conclusions point to a great improvement, mainly for solving elliptic differential equations and statistical functions.

Downloads

Download data is not yet available.

Author Biographies

  • Odirley Willians Miranda Saraiva, Regional University of the Northwest of the State of Rio Grande do Sul

    Graduated in Biology from the State University of Vale do Acaraú (UEVA) and Graduated in Physics from the Federal University of Pará (UFPA). Graduation in Mathematics (UEPA). Specialist in Science (UFPA) and in Mathematics Teaching (UEPA) Has experience in teaching Physics, Chemistry, Biology, Natural Sciences and Mathematics. Acting as a teacher since 2006 in Basic Education.

  • Gustavo Nogueira Dias, Federal College Ten. Rego Barros

    Doctor in Education from the National University of Rosario, Argentina (2017); Master in Geophysics from the Federal University of Pará, Belém (2011); Specialist in School Management by the University Center of Pará (2008); Full Degree in Mathematics from the Federal University of Pará (2001). Worked in private schools from 1991 to 2005. He joined SEDUC(PA) as a full professor from 2006 to 2016. , Science and Technology of Pará), in 2012. He also served as a professor with a scholarship at UFRA (Federal Rural University of the Amazon) in 2013. He joined UNAMA (University of the Amazon) as a professor from 2015 to 2016. of the Federal Elementary School of Colégio Ten. Rêgo Barros, which he joined in 2005 and from 2017 onwards he carries out his activities under the exclusive dedication regime. Participates in the study group GHEMAZ at UEPA, State University of Pará. He also works as a researcher in the areas: Environmental Science, Teaching and Learning, Mathematics Education, History of Mathematics, Mathematical Modeling, Administration, Accounting and Statistics.

  • Fabricio da Silva Lobato, Graduate Program in Mathematics Teaching

    Graduated in Mathematics from the University of the State of Pará (2014). He is currently a Mathematics teacher in Pre-Entrance Exam. Master's student at the Postgraduate Program in Mathematics Teaching at the University of the State of Pará (2019). Specialization in progress by Estácio in ENEM: SKILLS AND SKILLS IN MATHEMATICS AND NATURE SCIENCES. Specialization in progress at Estácio in Mathematics Teaching Methodology. Researching and publishing at a high level in the areas of Didactics of Mathematics, Distance Education (EAD) and Competences and Skills in Mathematics.

  • José Carlos Barros de Souza Júnior, Federal College Ten. Rego Barros

    Master's student at the State University of Pará. Graduated in Full Degree in Mathematics - State University of Pará (UEPA). Specialist in Mathematics in Basic Education. He is currently a mathematics teacher at Colégio Tenente Rêgo Barros.

  • Washington Luiz Pedrosa da Silva Junior, Federal College Ten. Rego Barros

    Licensed professor in Mathematics at the State University of Pará - UEPA. Specialist in Fundamentals of Elementary Mathematics, Educational Management and Teaching of Basic and Higher Education, Financial Mathematics, Statistics and Education in the Field and Brazilian Anthropology (ongoing). Professor at the Federal College Tenente Rêgo Barros- CTRB.

  • Cássio Pinho dos Reis, Federal University of Mato Grosso of South

    Bachelor in Statistics from the Federal University of Pará (2007), Master in Applied Statistics and Biometrics from the Federal University of Viçosa (2013) and Ph.D. in Biometrics from the Universidade Estadual Paulista - Botucatu (2019). He is currently Adjunct Professor A, level 1, at the Federal University of Mato Grosso do Sul. He teaches Statistics, Probability and Statistics, Biostatistics, Zootechnical Experimentation and Experimental Statistics. He has experience in Experimental Statistics, Regression and Correlation Analysis and Spatial Statistics.

  • Rondineli Carneiro Loureiro, Municipal Department of Education in Belém.

    Graduated in Mathematics from the State University of Pará (2002) and Master's in Mathematics from the Federal University of Pará (2015). He is currently ad-4-Executive Secretary of Education teacher and teacher-Municipal Secretary of Education in Belém. He has experience in Mathematics, with an emphasis on Mathematics

  • Herson Oliveira da Rocha, Federal Rural University of the Amazon

    Herson Rocha has a degree in Mathematics from the State University of Pará (UEPA, 2005), a master's degree in Geophysics from the Geosciences Institute of the Federal University of Pará (IG/UFPA, 2012), and a Ph.D. in Reservoir and Exploration Engineering from the Laboratory of Petroleum Engineering and Exploration at the State University of Norte Fluminense Darcy Ribeiro (LENEP/CCT/UENF, 2020). He is also a member of the Brazilian Society of Geophysics (SBGf) and the European Association of Geoscientists & Engineers (EAGE). He currently holds the position of adjunct professor at the Federal Rural University of Amazônia (UFRA).

  • Wagner Davy Lucas Barreto, Federal College of Aeronautics Tenente Rego Barros

    Graduated in Mathematics from the Federal University of Pará (2009) , and in science from the State University of Maranhão (2008). Specialist in Didactics of Mathematics by UFPA, Master's Degree in Mathematics in National Network by the Federal University of Pará (2020). Master in Environmental Sciences from the University of Taubaté (2012) . He is currently an instructor professor at the Air Force Command at Colégio Tenente Regô Barros CTRB and adjunct professor at Faculdade Pan Amazônica FAPAN. Has experience In preparation for the Mathematical Olympiad, has experience in primary, secondary and higher education in face-to-face and distance education

  • Antonio Thiago Madeira Beirão, Federal College of Aeronautics Tenente Rego Barros

    He holds a PhD (2018) and a Master's (2014) from the Graduate Program in Electrical Engineering at the Federal University of Pará (UFPA). Specialization in Contemporary Physics (2012), Bachelor's Degree in Physics (2018) and Degree in Mathematics (2010) all from the Federal University of Pará (UFPA). In addition, he has a degree in Physics (2009) from the Federal Institute of Education, Science and Technology of Pará (IFPA). He has experience in Condensed Matter Physics, acting mainly on the following topics: (i) Electronic Transport using Green out of balance (NEGF) formalism in the presence of Majorana Fermions; (ii) Electronic Transport in 2D allotropes of carbon under the effects of hydrogenation and doping; (iii) Teaching Physics using active methodologies and digital technologies. He is currently an Adjunct Professor at the Federal Rural University of Amazonia-UFRA.

  • Katiane Pereira da Silva, Rural Federal University of Amazon

    Graduated in Licenciatura in Natural Sciences - Physics from the University of the State of Pará (2006). Master in Physics from the Federal University of Maranhão (2010). PhD in Physics from the Federal University of Ceará (2014) with a PhD internship (sandwich) from the Institut de Cièncias de Materials de Barcelona (with research in semiconductor materials). She is currently an Adjunct Professor at the Federal Rural University of the Amazon - Campus Belém. She has experience in the area of Condensed Matter Physics in the experimental area, working mainly on the following topics: optical and structural properties of materials, using mainly the techniques of Raman Spectroscopy and Spectroscopy Infrared. Application of high hydrostatic pressures to organic and inorganic materials, X-ray diffraction and Rietveld refinement method

  • Nazaré Doriene de Melo Reis, Estácio do Para Faculty

    Degree in ACCOUNTING SCIENCES from the University of Amazônia (2005). He is currently studying Law at Faculdade Estácio do Pará. He has a postgraduate degree in TAX MANAGEMENT at Faculdade Ideal (FACI), and in STRATEGIC ADMINISTRA-TION at Faculdade Uniamericas (2014). She is currently Coordinator of the Accounting Sciences Course and professor at FACULTY ESTÁCIO DO PARA, MA in Administration from Universidad San Lorenzo (2015), and MA in Education from Universidade Metodista (2015). She is currently a Full University Professor at Faculdade Estácio do Pará (FAP) and an accountant and partner at MS CONTABILIDADE LTDA. He has experience in the field of Accounting Sciences, with an emphasis on Tax Management, Personnel and Accounting, working mainly on the following topics: Commercial and Financial Accounting, Management Accounting, Cost Accounting, Structures of Financial Statements, Computerized Practices, Management of Labor Practices , Tax Accounting and General Accounting.

References

Boyer, C. B. (2003).História da Matemática. São Paulo: Edgard Bencher Ltda.

Dana, P. W. (1993). Non Elementary Functions Antiderivatives, Article.

Eves, H. (2011). Introdução à história da matemática / Howard Eves; tradução Hygino H. Domingues. 5a ed. – Campinas, SP: Editora da Unicamp.

Gauss, C. F. (1798). Disquisitiones Arithmeticae.

Gonçalves, M. B.& Flemming, D. M. (2012). Funções de várias variáveis, integrais múltiplas, integrais curvilíneas e de superfície.2ª edição. Ed. Pearson.

Guidorizzi, H. L. (2005). Um Curso de Cálculo, Vol. 1 2, 3 e 4. 5ª ed., Ed. LTC.

Joseph, G. G. (1991). The crest of the peacock: Non-European roots of mathematics.

Princeton, NJ: Princeton University Press.

Pereira, A. S., et al. (2018). Metodologia da pesquisa científica. [e-book]. Santa Maria. Ed. UAB/NTE/UFSM.

Nóbrega, B. S. (2012). Análise Numérica para Integrais Não elementares.

Roque, T. (2012). Uma visão crítica: Desfazendo mitos e lendas, Editora Zahar.

Simmons, G. F. (2009). Cálculo com Geometria Analítica, Vol. 2, McGraw-Hill.

Stewart, J.(2013). Cálculo, volume II / James Stewart, 7ª edição. São Paulo: Cengage Learning.

Downloads

Published

2021-09-01

Issue

Vol. 9 No. 9 (2021): International Journal for Innovation Education and Research

Section

Journal Articles

License

Copyright (c) 2021 Odirley Willians Miranda Saraiva, Gustavo Nogueira Dias, Fabricio da Silva Lobato, José Carlos Barros de Souza Júnior, Washington Luiz Pedrosa da Silva Junior, Cássio Pinho dos Reis, Rondineli Carneiro Loureiro, Herson Oliveira da Rocha, Wagner Davy Lucas Barreto, Antonio Thiago Madeira Beirão, Katiane Pereira da Silva, Nazaré Doriene de Melo Reis

Creative Commons License

This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

Copyrights for articles published in IJIER journals are retained by the authors, with first publication rights granted to the journal. The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author for more visit Copyright & License.

How to Cite

Saraiva, O. W. M. ., Dias, G. N., Lobato, F. da S., Souza Júnior, J. C. B. de, Silva Junior, W. L. P. da, Reis, C. P. dos, Loureiro, R. C., Rocha, H. O. da, Barreto, W. D. L. ., Beirão, A. T. M., Silva, K. P. da, & Reis, N. D. de M. (2021). Integration method of non-elementary exponential functions using iterated Fubinni integrals. International Journal for Innovation Education and Research, 9(9), 169-177. https://doi.org/10.31686/ijier.vol9.iss9.3326
Received 2021-07-19
Accepted 2021-08-03
Published 2021-09-01
Crossref
Scopus
Google Scholar
Europe PMC

Most read articles by the same author(s)