Numerical integration involves calculation of an integral by numerical techniques. An integral is a mathematical representation of an area or generalization of an area and is one of the fundamental objects of calculus. The word quadrature can mean the numerical computation of an integral containing only one variable. Gaussian quadratures and Newton-Cotes formulas are methods of numerical integration. Cubature means the numerical computation of a multiple integral, a set of integrals taken over multiple variables, and includes Monte Carlo integration.

The main difference between the two classifications of numerical integration methods, Gaussian quadratures and Newton-Cotes formulas, is the way a curve is divided into parts for analysis. Gaussian quadratures provide flexibility and efficiency for known smooth functions but Newton-Cotes formulas are the most widely used numerical integration methods. All Gaussian quadratures involve evaluating an integral by the summation of the product of the function evaluated at...