Numerical calculation of double integrals with non-rectangular regions
Article Sidebar
Main Article Content
Abstract
Introduction. - In Mathematical Analysis, integrals are sometimes difficult to solve by integration methods, for this reason it is necessary to think of numerical methods to solve them, if these are definite integrals, even more so when it comes to double integrals. Objective: The ability to solve these integrals depends a lot on the solution knowledge and experience, for this reason the present study presents an alternative solution by numerical methods. Methodology: A double integral conceptually calculates the volume bounded by a surface over a region, the region may be rectangular or non-rectangular. The present study solves the type of indifferently, for which partitions are made along x and y of the region, thus showing a mesh within points (x,y) of the region, which are evaluated in the function f(x,y), which represents the surface, Results: with these values the integral is solved horizontally using the Simpson method and with the result of these it is solved vertically with the same method, obtaining the result of the double integral with excellent precision, Conclusions: a method of calculating double integrals is then proposed with numerical calculation for rectangular or non-rectangular regions.
Downloads
Article Details
References
Briones, J. (2015). Guía de Microsoft Excel. Revista Plena Inclusión, 3. https://www.plenainclusion.org/wp-content/uploads/2022/02/Plena-inclusion-Murcia.-Guia-de-Excel.pdf
Campuzano, A. (2016). Calculo Numérico Teoría, problemas y algunos programas con Máxima (Primera). https://repositorio.upct.es/bitstream/handle/10317/5377/isbn9788460878674.pdf
Chapra, S., & Canale, R. (2015). Métodos numéricos para ingenieros (Séptima Edición). Mc Graw Hill Education. https://www.academia.edu/40452797/M%C3%A9todos_num%C3%A9ricos_para_Ingenieros_7ma_Edici%C3%B3n_Chapra
Cortés Rosas, J. J., González Cárdenas, M. E., Pinilla Morán, V. D., Salazar Moreno, A., & Tovar Pérez, V. H. (2019). Aproximación numérica y errores. Revista UNAM, 1-16. https://www.ingenieria.unam.mx/pinilla/PE105117/pdfs/tema1/1_aproximacion_numerica_y_errores.pdf
Font, J. (2010). Integrales dobles y triples (pp. 206-209). ESP Ghostscript (Ed.). https://repositori.uji.es/xmlui/bitstream/handle/10234/7274/integraldoble0910.pdf?sequence=1
GeoGebra Team. (2023, agosto 5). Vista 3D - GeoGebra Manual. Vista 3D - GeoGebra Manual. https://wiki.geogebra.org/es/Vista_3D
Hurtado, N., & Sánchez, D. (2014). Métodos numéricos aplicados a la Ingeniería. Grupo Editorial Patria. https://www.academia.edu/35215572/Metodos_Numericos_Aplicados_a_La_Ingenieria_4a_Nieves
Lehman, C. (1989). Geometría Analítica (Decimatercera Edición). Limusa. https://www.cimat.mx/ciencia_para_jovenes/bachillerato/libros/[Lehmann]GeometriaAnalitica.pdf
Leithold, L. (1998). El cálculo (Séptima Edición). Oxford University Press. http://kali.azc.uam.mx/clc/03_docencia/leithold.pdf
Rodríguez Gómez, G., Gil Flores, J., & García Jiménez, E. (1996). Metodología de la investigación cualitativa. Ed. Aljibe, Málaga. https://www.researchgate.net/publication/44376485_Metodologia_de_la_investigacion_cualitativa_Gregorio_Rodriguez_Gomez_Javier_Gil_Flores_Eduardo_Garcia_Jimenez
Strang, G., & Herman, E. (2023). Integrales dobles sobre regiones rectangulares—Cálculo volumen 3 | OpenStax. https://openstax.org/books/cálculo-volumen-3/pages/5-1-integrales-dobles-sobre-regiones-rectangulares
Thomas, G. (2012). Cálculo Varias Variables (Decimosegunda Edición). Pearson Educación. https://robertocastellanos.com/Libros/Calculo%20Varias%20Variables%20-%20Thomas%2012Edicion.pdf
Villena, M. (2009). Integración Múltiple (pp. 150-152). Acrobat Distiller (Ed.). https://www.dspace.espol.edu.ec/bitstream/123456789/7287/5/5-Integraci%C3%B3n%20M%C3%BAltiple.pdf
Wrtaques. (2012). Funciones. En Funciones gráficas. PDFCreator (Ed.). http://biblio3.url.edu.gt/Libros/2012/calc/1.pdf