Integral Calculus

Abstract

Although much attention is given to differentiation in standard textbooks, and indeed, in this work book, we must not forget the role played by integration. Integration enables us to recover a function such as that of total revenue from marginal revenue or total cost from marginal cost. It also allows us, for example, to evaluate the revenue received over a given time period or to ascertain the value of consumer’s surplus and producer’s surplus from demand and supply curves, respectively. Unfortunately for us, integration can be rather more involved than differentiation. You may have thought that finding the answers to a crossword was bad enough (differentiation), but how about working from the answers to the clues? (integration). There are functions which are deceptively simple in appearance, but whose integrals are very complex. In this chapter, I shall concentrate on the simpler cases of integration which can be accomplished by simply reversing the corresponding formulae for differentiation. For more complicated cases, there are tables of standard integrals available in most texts on calculus. One such table is given in Weber, page 455. There is one good thing about integration, and that is you can always check your answer; simply differentiate what you think to be the answer and it should match up with what you are trying to integrate. If not, then you will have to think again.