Fundamentals of University Mathematics, 3rd Edition

Chapter 16

Integration—Methods and Applications

In Chapter 14, we introduced indefinite integrals and in Chapter 15, we extended the list of functions we can integrate. At this point, we can only integrate those functions in Appendix E and linear combinations of them.

In the first four sections of this chapter, we introduce methods which extend further the list of functions we can integrate. The first method, and probably the most useful, is substitution. It is based on the chain rule for differentiation. In Sections 16.2 and 16.3 we show how the method allows us to integrate rational functions and certain trigonometric functions. The discussion of t-formulae is of considerable theoretical interest. They show that certain trigonometric integrals ...