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HP -32S Owner's Manual Page 277

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fCxJ
-*- X
With this number of sample points, the algorithm will calculate the
same approximation for the integral of any of the functions shown.
The actual integrals of the functions shown with solid and dashed
lines are about the same, so the approximation will be fairly accurate
if f(x) is one of these functions. However, the actual integral of the
function shown with a dotted line is quite differentfrom those of the
others, so the current approximation will be ratherinaccurate if f(x) is
this function.
The algorithm comes to know the general behavior of the function by
sampling the function at more and more points. Ifa fluctuation of the
function in one region is not unlike the behavior over the rest of the
interval of integration, at some iteration the algorithm will likely de
tect the fluctuation. When this happens, the number of sample points
is increased until successive iterations yield approximations that take
into account the presence of the most rapid, but characteristic,
fluctuations.
For example, consider the approximation of
r
xe~xdx.
Since you're evaluating this integral numerically, you might think that
you should represent the upper limit of integration as 10499, which is
virtually the largest number you can key into the calculator. Try it and
see what happens. Enter this program that evaluates the function
f(x) = xe~x.
D: More About Integration
275

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