The Integral Calculus

Abstract

The differential as explained and interpreted in Chapter 3 takes very small changes in the variables concerned. The underlying method was to relate the rate of change in one variable to the rate of change in another. Like many other operations in mathematics, differentiation can be reversed. The reverse of differentiation is called integration. The objective is to find the whole of something when given only a ‘part’ of it. This ‘part’ has been called dy and what we want to find is Y as a function of X. Integration is the method that accomplishes this. For example, the derivative of Y when it is a function of X is

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and is called the ‘differential equation’. This can be rewritten

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