HP HP-15C - Page 246

246 Appendix E: A Detailed Look at f
)(δ)()(
2
xxfxF 
,
where 
2
(x) is the uncertainty associated with f(x) that is caused by the
approximation to the actual physical situation.
Since
)(δ)(

)(
1
xxfxf 
, the function you want to integrate is
)(δ)(δ)(

)(
21
xxxfxF 
or
)(δ)(

)( xxfxF 
,
x) is the net uncertainty associated with f(x).
Therefore, the integral you want is
dxxxfdxxF
b
a
b
a
)](δ)(

[)( 
 


b
a
b
a
dxxdxxf )()(


 I
where I is the approximation to

b
a
dxxF )(
    
associated with the approximation. The f algorithm places the number I
in the X--register.
The uncertainty (x) of
)(

xf
, 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