HP 15c Scientific manual Using f in a Program, 382

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	00	Return approximation to
	5		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.)