numerical integration is the term used for a number of methods to find an approximation for an integral. numerical integration has also been called quadrature. very often, it is not possible to solve integration analytically, for example when the data consists of a number of distinct measurements, or when the antiderivative is not known, and it is difficult, impractical or impossible to find it. in such cases, the integral can be written as a mathematical function defined over the interval in question, plus a function giving the error.