Applications of complex variable residue theory to the evaluation solution of irrational definite integrals. II
type: Item
instance of: scholarly article
title: Applications of complex variable residue theory to the evaluation solution of irrational definite integrals. II
zbMATH Open document ID: 0722.30024
DOI: 10.1016/0096-3003(90)90028-2
author: James Evans
published in: Applied Mathematics and Computation
publication date: 1990-01-01T00:00:00Z
review text: The author shows that eight definite integrals, whose integrands contain the square root of expressions involving trigonometric functions, are zero. The reason for publishing the paper is not clear. The technique has already been given [ibid. 36, No.3, 163-172 (1990; Zbl 0699.33002)], and the values of the integrals are easily found (each integral can be transformed to one with an odd integrand over a symmetric interval). For the validity of the analysis of the first integral, \[ \int^{2\pi}_{0}\sin \sigma (a+\cos \sigma)^{1/2}d\sigma, \] it is necessary that \(a>1\). This condition is not imposed here or later where it is also needed.
reviewed by: D. Kershaw
Mathematics Subject Classification ID: 30E20
Mathematics Subject Classification ID: 65D30
Mathematics Subject Classification ID: 33E20
zbMATH DE Number: 4190105
zbMATH Keywords: definite integrals
MaRDI profile type: Publication
full work available at URL: 0096-3003(90)90028-2
OpenAlex ID: W4254338482
cites work: Evaluation of four irrational cosine definite integrals using residue theory
cites work: Evaluation of four irrational definite sine integrals using residue theory
cites work: Q4757980
cites work: Q3267573
cites work: Q5328659
description: scientific article; zbMATH DE number 4190105