ABSTRACT
This chapter introduces the basic ideas underlying the definite integral, and aims to provide a theorem that shows how definite integrals can be evaluated by using the idea of differentiation in reverse. It is concerned with the theory of the operation known as integration, which occupies a central position in the calculus. In mechanics the concepts of the centre of mass and moment of inertia of a body are both of considerable importance, and in general they rely for their determination on the techniques of integration. If the body comprises a system of discrete masses, each rigidly positioned relative to the others, and then only a summation is involved in the computation. The fact that an antiderivative is a function related to the operation of integration, and not just a number as is an ordinary definite integral, is indicated by again employing the integral sign, but this time without limits.
