HP HP-15C, Руководство пользователя

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246 Appendix E: A Detailed Look at
f
) (
δ
) ( ) (
2
x x f x F
 
,
where δ
2
( x ) is the uncertainty associated with f(x) that is caused by the
approximation to the actual physical situation.
Since
) (
δ
) (
ˆ
) (
1
x x f x f
 
, the function you want to integrate is
) (
δ
) (
δ
) (
ˆ
) (
2 1
x x x f x F
  
or
) (
δ
) (
ˆ
) ( x x f x F
 
,
where δ(
x ) is the net uncertainty associated with f(x) .
Therefore, the integral you want is
dx x x f dx x F
b
a
b
a
)] (
δ
) (
ˆ
[ ) (
 
 
 
 
b
a
b
a
dx x dx x f ) ( ) (
ˆ

  
I
where I is the approximation to
 b
a
dx x F ) (
and ∆ is the uncertainty
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
x f
, 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