ABSTRACT
Numerical integration is 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. Approximate methods of definite integrals may be determined by what is termed numerical integration. Three methods of finding approximate areas under curves are the trapezoidal rule, the mid-ordinate rule and Simpson's rule, and these rules are used as a basis for numerical integration. In general, Simpson's rule is regarded as the most accurate of the three approximate methods used in numerical integration. The appropriate combination of the two in Simpson's rule eliminates this error term, giving a rule which will perfectly model anything up to a cubic, and have a proportionately lower error for any function of greater complexity. In general, for a given number of strips, Simpson's rule is considered the most accurate of the three numerical methods.
