The definite integrals of 2- refined neutrosophic functions and its properties by Yaser Ahmad Alhasan, Mohamed Elghazali Ali Mohieldin Mohamed, Raja Abdullah Abdulfatah

Subjects: “…definite integrals…”
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Exploring concepts of definite integrals in two variables using GeoGebra by Pitágoras Pinheiro de Carvalho, Afonso Norberto da Silva, Maria da Cruz Vieira da Silva, William Fernando da Silva Rodrigues

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Definite Integrals Involving Combinations of Powers and Logarithmic Functions of Complicated Arguments Expressed in Terms of the Hurwitz Zeta Function by Robert Reynolds, Allan Stauffer

“…A summary of the results is produced in the form of a table of definite integrals for easy referencing by readers.…”
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DEFINITE INTEGRAL OF LOGARITHMIC FUNCTIONS AND POWERS IN TERMS OF THE LERCH FUNCTION by Robert Reynolds, Allan Stauffer

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The evaluation of a definite integral by the method of brackets illustrating its flexibility by Gonzalez Ivan, Santander John Lopez, Moll Victor H.

“…The method of brackets is a procedure to evaluate definite integrals over a half-line. It consists of a small number of rules. …”
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New expressions for certain polynomials combining Fibonacci and Lucas polynomials by Waleed Mohamed Abd-Elhameed, Omar Mazen Alqubori

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New Results for Certain Jacobsthal-Type Polynomials by Waleed Mohamed Abd-Elhameed, Omar Mazen Alqubori, Amr Kamel Amin

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Students’ visual thinking ability in solving the integral problem by Ummu Sholihah, Maryono Maryono, Maryono Maryono

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['Vector study of the definite integral for the analysis of fluid viscosity', 'Implementación de la integral definida para el análisis de la viscosidad de fluidos '] by Glorielí Ponce Herrera, Fátima Suyén López Valdivia, Carmen Isabel Canales Urrutia, Walter Ismael Medina Martínez, Cliffor Jerry Herrera Castrillo

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Truncation error estimation for Newton–Cotes quadrature formulas by Kostas Plukas, Danutė Plukienė

Subjects: “…definite integral…”
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Professionally oriented approach to the study of the section "integral calculus" in the training of specialists of the economic profile by Nataliya V. Spiridonova

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Reduction Formulae of 2-refined Neutrosophic Integrals and their Applications by Florentin Smarandache, Bishnupada Debnath

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On Certain Properties of a Univalent Function Associated with Beta Function by Matthew Olanrewaju Oluwayemi, Sunday Olufemi Olatunji, Temitope O. Ogunlade

“…Beta function has some applications in differential equations and other areas of sciences and engineering where certain definite integrals are used. However, its applications to univalent functions have not been explored based on the available literature. …”
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The Mellin Transform of Logarithmic and Rational Quotient Function in terms of the Lerch Function by Robert Reynolds, Allan Stauffer

“…We will use this transform to create a table of definite integrals which can be used to extend similar tables in current books featuring such formulae.…”
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Relation of the Cyclotomic Equation with the Harmonic and Derived Series by Luis J. Boya, Cristian Rivera

“…We associate some (old) convergent series related to definite integrals with the cyclotomic equation xm-1=0, for several natural numbers m; for example, for m=3, x3-1=(x-1)(1+x+x2) leads to ∫01dx(1/(1+x+x2))=π/(33)=(1-1/2)+(1/4-1/5)+(1/7-1/8)+⋯. …”
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Quantum Inequalities of Hermite–Hadamard Type for r-Convex Functions by Xuexiao You, Hasan Kara, Hüseyin Budak, Humaira Kalsoom

“…In this present study, we first establish Hermite–Hadamard type inequalities for r-convex functions via qκ2-definite integrals. Then, we prove some quantum inequalities of Hermite–Hadamard type for product of two r-convex functions. …”
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On generalized Hermite polynomials by Waleed Mohamed Abd-Elhameed, Omar Mazen Alqubori

“…The first application is concerned with introducing some weighted definite integrals involving the GHPs. In contrast, the second is concerned with establishing the operational matrix of the integer derivatives of the GHPs.…”
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On the Origins of Hamilton’s Principle(s) by Paolo Bussotti, Danilo Capecchi, Giuseppe Ruta

“…We consider the investigations on geometrical optics in the 17th and 18th centuries, Euler’s and Lagrange’s foundations of variational calculus in the 18th century to find extrema of physical quantities expressed as infinite sums of infinitesimals (today, we would say ‘definite integrals’), and Lagrange’s introduction of a revolutionary analytical mechanics, all of which are all fertile grounds for Hamilton’s steps—first, in what we could call analytical optics, then in an advanced form of analytical mechanics. …”
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Spectral tau technique via Lucas polynomials for the time-fractional diffusion equation by Waleed Mohamed Abd-Elhameed, Abdullah F. Abu Sunayh, Mohammed H. Alharbi, Ahmed Gamal Atta

“…The discretization of the technique is based on several formulas about Lucas polynomials, such as those for explicit integer and fractional derivatives, products, and certain definite integrals of these polynomials. These formulas aid in transforming the TFDE and its conditions into a matrix system that can be treated through a suitable numerical procedure. …”
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Novel Expressions for Certain Generalized Leonardo Polynomials and Their Associated Numbers by Waleed Mohamed Abd-Elhameed, Omar Mazen Alqubori, Abdulrahim A. Alluhaybi, Amr Kamel Amin

“…Additionally, new product formulas involving the generalized Leonardo polynomials with the Fibonacci and Lucas polynomials are provided, along with computations of definite integrals based on the derived formulas.…”
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