Investigation and Analysis of Newton-Cotes Integration Formulas and Errors from Two up to Eight Nodes Using Lagrange Interpolation

Much research has been done regarding the Newton Coates method and generally the results that are available are about the trapezoidal method and the Sampson method and not much attention is paid to the higher levels of the Newton Coates method. This article has been written to find out what is the relationship between the high-order Newton-Cotes method and study behavior of error in high order methods. In this research numerical integration preformed, Newton Coates method is examined in detail and formulate the two points, three points, four points up to eight points are will investigate. Furthermore, this study showed that, analyze the errors of each method and show the relation between two consecutive Newton Coates methods. On the other hand, the research showed that, odd point’s method would be better. It is worth mentioning that to obtain these methods, and in this study the researcher used the Lagrange interpolator polynomial.