ABSTRACT
At the end of this chapter, you should be able to:
• appreciate the need for numerical integration • evaluate integrals using the trapezoidal rule • evaluate integrals using the mid-ordinate rule • evaluate integrals using Simpson’s rule • apply numerical integration to practical situations
Even with advanced methods of integration there are many mathematical functions which cannot be integrated by analytical methods and thus approximate methods have then to be used. Approximatemethods of definite integrals may be determined by what is termed numerical integration. It may be shown that determining the value of a definite integral is, in fact, finding the area between a curve, the horizontal axis and the specified ordinates. 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.
