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246
Appendix E: A Detailed Look at
where δ
(x) is the uncertainty associated with f(x) that is caused by the
2
approximation to the actual physical situation.
( ˆ
Since
f
(
x
)
f
or
where δ(x) is the net uncertainty associated with f(x).
Therefore, the integral you want is
where I is the approximation to
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
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
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
–4
is ± 0.005×10
F
(
δ
, the function you want to integrate is
x
)
(
x
)
1
( ˆ
F
(
x
)
f
x
)
( ˆ
F
(
x
)
f
x
)
b
b
( ˆ
F
(
x
)
dx
[
f
a
a
b
( ˆ
f
a
I
( ˆ x
, the function calculated by your subroutine, is
f
)
–2
= ± 0.5×10
×10
f
δ
x
)
f
(
x
)
(
x
)
2
δ
δ
(
x
)
(
x
)
1
2
( δ
,
x
)
( δ
x
)
x
)]
dx
b
x
)
dx
(
x
)
dx
a
b
F )
(
x
dx
a
–04.
–4
= ± 0.5×10
,
and ∆ is the uncertainty
-6
. Thus, setting the display
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