HP 15c - Manual (Page 203)

Section 14: Numerical Integration 203
In the preceding example, the uncertainty indicated that the approximation
might be correct to only four decimal places. If we temporarily display all
10 digits of the approximation, however, and compare it to the actual value
of the integral (actually, an approximation known to be accurate to a
sufficient number of decimal places), we find that the approximation is
actually more accurate than its uncertainty indicates.
Keystrokes Display
® 1.382
5 00 Return approximation to
display.
´ CLEAR u 1382459676 All 10 digits of
approximation.
The value of this integral, correct to eight decimal places, is 1.38245969. The
calculator's approximation is accurate to seven decimal places rather than
only four. In fact, since the uncertainty of an approximation is calculated
very conservatively, the calculator's approximation, in most cases will be
more accurate than its uncertainty indicates. However, normally there is no
way to determine just how accurate an approximation is.
For a more detailed look at the accuracy and uncertainty of f
approximations, refer to appendix E.
Using f in a Program
f can appear as an instruction in a program provided that the program is
not called (as a subroutine) by f itself. In other words, f cannot be
used recursively. Consequently, you cannot use f to calculate multiple
integrals; if you attempt to do so, the calculator will halt with
Error 7 in the
display. However, f can appear as an instruction in a subroutine called
by _.
The use of f as an instruction in a program utilizes one of the seven
pending returns in the calculator. Since the subroutine called by f
utilizes another return, there can be only five other pending returns.
Executed from the keyboard, on the other hand, f itself does not utilize
one of the pending returns, so that six pending returns are available for
subroutines within the subroutine called by f Remember that if all seven
pending returns have been utilized, a call to another subroutine will result in
a display of
Error 5 . (Refer to page 105.)