Approximate integration through remarkable points using the Intermediate Value Theorem


Authors

DOI:

https://doi.org/10.22517/23447214.21641

Keywords:

Approximate Integration, Simpson’s Rule, Intermediate Value Theorem.

Abstract

Using the Intermediate Value Theorem we demonstrate the rules of Trapeze and Simpson's. Demonstrations with this approach and its generalization to new formulas are less laborious than those resulting from methods such as polynomial interpolation or Gaussian quadrature. In addition, we extend the theory of approximate integration by finding new approximate integration formulas. The methodology we used to obtain this generalization was to use the definition of the integral defined by Riemann sums. Each Riemann sum provides an approximation of the result of an integral. With the help of the Intermediate Value Theorem and a detailed analysis of the Middle Point, Trapezoidal and Simpson Rules we note that these rules of numerical integration are Riemann sums. The results we obtain with this analysis allowed us to generalize each of the rules mentioned above and obtain new rules of approximation of integrals. Since each of the rules we obtained uses a point in the interval we have called them according to the point of the interval we take. In conclusion we can say that the method developed here allows us to give new formulas of numerical integration and generalizes those that already exist.

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Author Biography

Jaime Castro Pérez, Instituto Tecnológico y de Estudiso Superiores de Monterrey CDMX

Profesor investigador del departamento de Ciencias del ITESM

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Published

2020-03-30

How to Cite

Castro Pérez, J., González Nucamendi, A., & Aguilar Sánchez, G. P. (2020). Approximate integration through remarkable points using the Intermediate Value Theorem. Scientia Et Technica, 25(1), 142–149. https://doi.org/10.22517/23447214.21641

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Section

Ciencias Básicas