Calculus (ii)—Integration and Differential Equations

Abstract

The last chapter showed simple business problems being solved by differentiation, the calculation at particular points of the rate at which a function changed in relationship to a variable, where the rate itself was in continuous change. Each calculation involved an analytical or ‘narrowing down’ process, conveniently summarised in the relationship

$$\mathop {FUNCTION \to DERIVATIVE}\limits_{(Differentiation)}$$

e.g. in Example 7.1, we have

$${X^2} \to 2X$$

This chapter considers the inverse relationship. We are given, for example 2X, and asked to state a function from which it was obtained by differentiation: and because we can recall or have recorded the process, we cab state X² as the required value. It is the integral of 2X, the connotation of the term indicating a process of expansion or building up, synthetical, instead of analytical. Chapter 7 gives other example.