For observed sound‐speed profiles, the range to a noise source in the first convergence zoneis calculated numerically by applying Gaussian quadrature techniques of various orders to the ray‐tracing range integral. The observed profile is tabulated for standardoceanographic depths. The tabulated profile is mapped into the sample set for Gaussian quadrature bycubic splines. We compare various strategies that divide the ray‐tracing range integral into convenient intervals for evaluation by the appropriate Gaussian quadrature consistentwith the singular points of the integrand.