HP 15c Scientific manual –04

246 Appendix E: A Detailed Look at f

F(x) = f (x) ± δ2 (x) ,

where δ2(x) is the uncertainty associated with f(x) that is caused by the approximation to the actual physical situation.

Since	ˆ
	f (x) = f (x) ± δ1(x) , the function you want to integrate is
	ˆ	± δ2	(x)
	F(x) = f (x) ± δ1(x)
or	ˆ
	F(x) = f (x) ± δ(x) ,

where δ(x) is the net uncertainty associated with f(x).

Therefore, the integral you want is

∫	b		b	ˆ
	F (x) dx = ∫		[ f (x) ± δ(x)]dx
a		a
		= ∫	b	ˆ	b
				f (x) dx ± ∫δ (x) dx
			a		a
		= I ±
					b
where I is the		approximation to			∫F (x) dx and ∆ is the uncertainty
					a

associated with the approximation. The f algorithm places the number I in the X-register and the number ∆ in the Y-register.

The uncertainty δ(x) of	ˆ
	f (x) , the function calculated by your subroutine, is

determined as follows. Suppose you consider three significant digits of the function's values to be accurate, so you set the display format to i 2. The display would then show only the accurate digits in the mantissa of a

function's values: for example, 1.23 –04.

Since the display format rounds the number in the X-register to the number displayed, this implies that the uncertainty in the function's values is ± 0.005×10–4= ± 0.5×10–2×10–4= ± 0.5×10-6. Thus, setting the display