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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
b
I
f
a
The
quantity
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.
Section 14
( dx
x
)
.
I
can
be
interpreted
*
194
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