Numerical integration

Summary

Numerical integration is the computation of approximate values of definite integrals from finitely many values of the integrand. It is needed when an antiderivative has no closed form or when the integrand is only known at sample points. It is also needed for integrals over domains of many dimensions. The main tools are quadrature rules, weighted sums of function values, together with error estimates based on the smoothness of the integrand.