Applications of complex variable residue theory to the evaluation solution of irrational definite integrals. II
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.
scientific article; zbMATH DE number 4190105