HP HP-15C

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.