Risk and the Theory of Security Risk Assessment by Carl S. Young

Author:Carl S. Young
Language: eng
Format: epub
ISBN: 9783030306007
Publisher: Springer International Publishing

The process of integration adds infinitesimally small pieces of a function dx′ to yield the area under the curve described by that function. If the function is constant in each variable, the integration becomes a straightforward addition or equivalently, a multiplication. But what if the value of a function is not constant? In that case, finding the area under the curve requires more than simple multiplication.

For example, calculating the area bounded by a rectangular function of constant length x and constant width y is accomplished by a straightforward multiplication of x times y. However, if the values of x and/or y vary, determining the area under the curve defined by the function requires a subtler approach. As noted above, Leibniz and Newton developed the approach independently in the seventeenth century.

At a high level, summing the entire function involves dividing it into infinitesimal pieces, dx and dy, and adding the pieces between the limits of the function. The so-called definite integral is a number that represents the result of a continuous summation of a function within defined limits. Figure 6.11 depicts the integration operation. In this case, the process of integration is used to determine the area under the curve I, defined by the varying function f(x) between the limits specified by the points A and B.

Fig. 6.11The definite integral

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