HP 15c - Manual (Page 200)

200 Section 14: Numerical Integration
Accuracy of f
The accuracy of the integral of any function depends on the accuracy of the
function itself. Therefore, the accuracy of an integral calculated using f
is limited by the accuracy of the function calculated by your subroutine.
*
To
specify the accuracy of the function, set the display format so that the
display shows no more than the number of digits that you consider accurate
in the function's values.
†
If you specify fewer digits, the calculator will
compute the integral more quickly;
‡
but it will presume that the function is
accurate to only the number of digits specified in the display format. We'll
show you how you can determine the accuracy of the calculated integral
after we say another word about the display format.
You'll recall that the HP-15C provides three types of display formatting:
•, i, and ^. Which display format should be used is largely a
matter of convenience, since for many integrals you'll get about the same
results using any of them (provided that the number of digits is specified
correctly, considering the magnitude of the function). Because it's more
convenient to use i display format when calculating most integrals,
we'll use i when calculating integrals in subsequent examples.
Note: Remember that once you have set the display format, you
can change the number of digits appearing in the display by storing
a number in the Index register and then pressing ´ • V,
´ i V, or ´ ^ V, as described in section 10.
This capability is especially useful when f is executed as part
of a program.
* It is possible that integrals of functions with certain characteristics (such as spikes or very rapid
oscillations) might be calculated inaccurately. However, this possibility is very small. The general
characteristics of functions that could cause problems, as well as techniques for dealing with them, are
discussed in appendix E.
†
The accuracy of a calculated function depends on such considerations as the accuracy of empirical
constants in the function as well as round–off error in the calculations. These considerations are discussed
in more detail in the HP-15C Advanced Functions Handbook.
‡
The reason for this is discussed in appendix E.