ABSTRACT
There are two main reasons for why there is a need to do numerical integration - analytical integration may be impossible or unfeasible, or it may be necessary to integrate tabulated data rather than known functions. There are many applications for integration. For example, Maxwell's equations can be written in integral form; numerical solutions of Maxwell's equations can be directly used for a huge number of engineering applications. Integration is involved in practically every physical theory in some way - vibration, distortion under weight or one of many types of fluid flow - be it heat flow, air flow, or water flow, and so on; all these things can be either directly solved by integration or some type of numerical integration. Numerical integration is also essential for the evaluation of integrals of functions available only at discrete points; such functions often arise in the numerical solution of differential equations or from experimental data taken at discrete intervals.
