numerical integration Algorithm

In analysis, numerical integration comprises a wide family of algorithms for calculate the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. Some writers refer to numerical integration over more than one dimension as cubature; others take quadrature to include higher-dimensional integration. In medieval Europe the quadrature meant calculation of area by any method. quadrature is a historical mathematical term that means calculate area. Mathematicians of Ancient Greece, according to the Pythagorean doctrine, understand calculation of area as the procedure of constructing geometrically a square have the same area (squaring).

numerical integration source code, pseudocode and analysis