ABSTRACT
In the physical and life sciences it is frequently the case that more information is available concerning the rate of change of a process than about the process itself. Translated into mathematical terms, this means that the derivative of a function may be known; the task is to find the function itself. The definite integral arises in an extraordinary variety of ways including such diverse situations as the calculation of surface areas, volumes, centers of gravity and of the work done by a variable force. The chapter examines the role of the integral in three rather distinct contexts: a problem in probability, the calculation of arc lengths of certain curves, and the formulation of an integral equation which is used to establish the existence and uniqueness of solutions of a wide class of first-order differential equations.
