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On numerical computation of integrals with integrands of the form f.x/sin.w=xr / on [0, 1]

A. Ihsan Hascelik
Journal / Anthology

Journal of Computational and Applied Mathematics
Year: 2009
Volume: 223
Issue: 1
Page range: 399-408

With existing numerical integration methods and algorithms it is difficult in general to obtain accurate approximations to integrals of the form Z 1 0 f .x/ sin  ! xr  dx or Z 1 0 f .x/ cos  ! xr  dx; .r > 0/ where f is a sufficiently smooth function on [0, 1]. Gautschi has developed software (as scripts in Matlab) for computing these integrals for the special case r D ! D 1. In this paper, an algorithm (as a Mathematica program) is developed for computing these integrals to arbitrary precision for any given values of the parameters in a certain range. Numerical examples are given of testing the performance of the algorithm/program.