HP 15c Scientific manual Accuracy of f

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 iwhen 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.