On spline-on-spline numerical integration formula (Q1263024)

In the paper is considered an application of the spline-on-spline interpolation to a numerical integration of the form \[ \int^{x_{j+1}}_{x_ j}f(x)dx\quad or\quad (\int^{x_{j+1}}_{x_ j}f(x)dx)/(\int^{1}_{0}f(x)dx) \] where \(j=0,1,...,n-1\). It is shown that an integral of the spline-on-spline interpoland gives better results than the spline itself. Some integration formulas are considered and compared. One numerical example is given.