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194

Section 14

Numerical Integration

Many problems in mathematics, science, and

engineering require calculating the definite

integral of a function. If the function is

denoted by f(x) and the interval of integration

is a to b, the integral can be expressed

mathematically as

.)( dxxfI



The quantity I can be interpreted

geometrically as the area of a region bounded by the graph of f(x), the

x-axis, and the limits x = a and x = b.

When an integral is difficult or impossible to evaluate by analytical

methods, it can be calculated using numerical techniques. Usually, this can

be done only with a fairly complicated computer program. With your

HP-15C, however, you can easily do numerical integration using the f

(integrate) key.



Using f

The basic rules for using f are:

1. In Program mode, key in a subroutine that evaluates the function f(x) that

you want to integrate. This subroutine must begin with a label

instruction (´b label) and end up with a value for f(x) in the X-

Provided that f(x) is nonnegative throughout the interval of integration.



The f function does not use the imaginary stack. Refer to the HP-15C Advanced Functions Handbook

for information about using f in Complex mode.

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