Since many planar boundary value problems of mathematical physics can be formulated as boundary integral equations, the numerical evaluation of line integrals is of great interest.
The authors consider a simple method for the calculation of line integrals over smooth curves. The method consists in first replacing a parametrization of the curve by a piecewise polynomial interpolant of it and then in using a Newton-Cotes quadrature rule.
The remarkable result pointed out by the authors is that the order of convergence of the resulting quadrature formula is higher than would be expected on the basis of interpolation theory.
The paper concludes with a numerical illustrative example.