Appendix E: A Detailed Look at
f
243
The uncertainty indicates that the displayed digits of the approximation
might not include any digits that could be considered accurate. Actually,
this approximation is more accurate than its uncertainty indicates.
Keystrokes
Display
®
7.79 -03
Return
approximation
to
display.
´
CLEAR
u
(hold)
7785820888
All 10 digits of
i
2
approximation.
The actual value of this integral, correct to five significant digits, is
7.7805×10
-3
. Therefore, the error in this approximation is about
(7.7858
7.7805)×10
-3
= 5.3×10
-6
.
This error is considerably less than the
uncertainty, 1.45×10
-3
The uncertainty is only an
upper bound
on the error
in the approximation; the actual error will generally be smaller.
Now calculate the integral in
i
3 and compare the accuracy of the
resulting approximation to that of the
i
2 approximation.
Keystrokes
Display
´
i
3
7.786 –03
Changes display format
to
i
3.
)
)
3.142 00
Rolls down stack until
upper limit appears in X-
register.
´
f
0
7.786 –03
Integral approximated in
i
3
®
1.448 –04
Uncertainty of
i
3
approximation.
®
7.786 –03
Returns approximation to
display.
´
CLEAR
u
(hold)
7785820888
All 10 digits of
i
3 approximation.
Summary of Contents for HP-15C
Page 1: ...HP 15C Owner s Handbook HP Part Number 00015 90001 Edition 2 4 Sep 2011 ...
Page 17: ...Part l HP 15C Fundamentals ...
Page 64: ......
Page 65: ...Part ll HP 15C Programming ...
Page 118: ...118 ...
