At the request of the definite integral of some function ， the original function is very complex and difficult to find the elementary function expression ， the integral is difficult to accurately calculate ， only managed to find the approximate value ， and allows direct interface with the Newton - Leibniz formula the case of the definite integral is small Numerical integration is an effective method to solve such problems The numerical integration is an important branch of numerical analysis ; therefore， explore the approximate calculation of the numerical integration method has obvious practical significance Departure from the numerical integration problem ， described in detail some of the numerical integration method This paper has detailed description of the Newton - Coates quadrature formula ， and in order to improve the precision of the integral calculation accuracy of numerical integration formulas ， Romberg quadrature formulas and the Gauss - Legendre quadrature formula In addition to the study of these numerical integration algorithm theory ， the article also compares these numerical integration algorithm by matlab program on your computer ， and an example quadrature formula with a variety of operations， analysis and comparison of various quadrature formula calculation error
