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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
I =
b
a
f (x) dx.
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-register.
*
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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