Accuracy Of The Function To Be Integrated; Functions Related To Physical Situations - HP -15C Advanced Functions Handbook

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Section 2: Working With (7F] 47
sin x ,
- ax
won't be interrupted by division by zero at an endpoint. Second, [7T|
can integrate functions that behave like \/\x — a\ whose slope is
infinite at an endpoint. Such functions are encountered when
calculating the area enclosed by a smooth, closed curve.
Another refinement is that [W\s extended precision, 13
significant digits, to accumulate the internal sums. This allows
thousands of samples to be accumulated, if necessary, without
losing to roundoff any more information than is lost within your
function subroutine.
Accuracy of the Function to be Integrated
The accuracy of an integral calculated using |"/T| depends on the
accuracy of the function calculated by your subroutine. This
accuracy, which you specify using the display format, depends
primarily on three considerations:
• The accuracy of empirical constants in the function.
• The degree to which the function may accurately describe a
physical situation.
• The extent of round-off error in the internal calculations of the
calculator.
Functions Related to Physical Situations
Functions like cos(40 — sin 6) are pure mathematical functions. In
this context, this means that the functions do not contain any
empirical constants, and neither the variables nor the limits of
integration represent actual physical quantities. For such
functions, you can specify as many digits as you want in the
display format (up to nine) to achieve the desired degree of
accuracy in the integral.* All you need to consider is the trade-off
between the accuracy and calculation time.
* Provided that f(x) is still calculated accurately, despite round-off error, to the number of
digits shown in the display.