Numerical Integration

Abstract

The objective of this chapter is to derive and then test methods that can be used to evaluate the definite integral In most calculus textbooks the examples and problems dedicated to integration are not particularly complicated, although some require a clever combination of methods to carry out the integration. In the real world the situation is much worse. As an example, to find the deformation of an elastic body when compressed by a rigid punch it is necessary to evaluate (Gladwell [1980] Moreover, it is relatively easy to find integrals even worse than the one above. To illustrate, in the study of the emissions from a pulsar it is necessary to evaluate (Gwinn et al. [2012] where K2 is the modified Bessel function. The point here is that effective numerical methods for evaluating integrals are needed, and our objective is to determine what they are.