Error bounds for approximations of the definite integrals
type: Item
instance of: scholarly article
title: Error bounds for approximations of the definite integrals
zbMATH Open document ID: 1007.65014
author: Gou-Sheng Yang
author: Jen-Chun Fang
author: Su-Shing Ling
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2003-03-09T00:00:00Z
review text: This paper is concerned with the approximation of the Riemann integral \(\int _a^bf(x) dx \) of a differentiable function \(f\) by the classical trapezoidal, midpoint and Simpson rules. The authors show that the errors are of first order accuracy and depend only on \(||f^\prime ||\). Bounds for the error terms are also given for a convex function \(f\) in the case that both \(m=\int _+^\prime f(a)\) and \(M=\int _-^\prime f(b)\) exist.
reviewed by: Luigi Gatteschi
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A80
zbMATH DE Number: 1786049
zbMATH Keywords: trapezoidal rule
zbMATH Keywords: mid-point rule
zbMATH Keywords: Simpson rule
zbMATH Keywords: inequalities for definite integrals
zbMATH Keywords: error bounds
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1786049