SciPy Recipes

Computing integrals using the Newton-Cotes method

The implementation of these two algorithms does not compute the interpolators explicitly. The final formulas are the target here, and the way it is coded in SciPy is by means of Newton-Cotes quadratures.

The routines to perform Newton-Cotes are hidden (in the sense that they are not reported in the tutorials or documentation in the official pages of SciPy) and are meant to be used only internally by cumtrapz or simps. They provide only the corresponding coefficients that multiply the function evaluation at the nodes.

However, Newton-Cotes quadrature formulas are usually very accurate by themselves in the right scenarios. They can be used to compute better approximations in many cases, without ...