A new algorithm for integral of trigonometric functions with mechanization
type: Item
instance of: scholarly article
title: A new algorithm for integral of trigonometric functions with mechanization
zbMATH Open document ID: 1069.65149
author: Weiming Wang
author: Changsheng Lin
published in: Applied Mathematics and Computation
publication date: 2005-05-04T00:00:00Z
review text: The authors systematically study the problem of integration of a rational expression \(R(\sin x,\cos x)\) by the substitution \(t = \tan {x \over 2}\). They observe that the resulting function \(F(\tan {x \over 2})\) has jump discontinuities at \(2k\pi + \pi\) \((k\in {\mathbb Z})\). If \(F(-)\), \(F(+)\) are the left- and right-hand limits of \(F(\tan {x\over 2})\) at \(2k\pi + \pi\) \((k\in {\mathbb Z})\), then a primitive function of \(R(\sin x, \cos x)\) reads as follows \(G(x) = F(\tan {x \over 2}) - F(-)\) for \(x \in [2k\pi,\, 2k\pi + \pi)\), \(G(2k\pi + \pi) = 0\), \(G(x)= F(\tan {x \over 2}) + F(+)\) for \(x \in (2k\pi + \pi,\, 2k\pi +2\pi]\) \((k \in {\mathbb Z})\). Further a new Maple program for the integration of \(R(\sin x, \cos x)\) is proposed.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 26A36
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 42A10
zbMATH DE Number: 2165260
zbMATH Keywords: indefinite integral
zbMATH Keywords: primitive function
zbMATH Keywords: antiderivative
zbMATH Keywords: trigonometric function
zbMATH Keywords: rational expression
zbMATH Keywords: substitution
zbMATH Keywords: Maple program
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: j.amc.2004.04.096
OpenAlex ID: W2036055775
cites work: Q5333460
cites work: Q4115333
cites work: Q4321740
cites work: Basic principles of mechanical theorem proving in elementary geometries
cites work: Mechanical theorem proving in geometries. Basic principles. Transl. from the Chinese by Xiaofan Jin and Dongming Wang
cites work: Q4545702
DOI: 10.1016/J.AMC.2004.04.096
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description: scientific article; zbMATH DE number 2165260