HP 15c - Manual (Page 251)

Appendix E: A Detailed Look at
f
251
Since you’re evaluating this integral numerically, you might think (naively
in this case, as you'll see) that you should represent the upper limit of
integration by 10
99
– which is virtually the largest number you can key into
the calculator. Try it and see what happens.
Key in a subroutine that evaluates the function f(x) = xe
-x
Keystrokes Display
|¥ 000-
Program mode.
´ b 1 001-42,21, 1
“ 002- 1 6
' 003- 12
* 004- 20
| n 005- 43 32
Set the calculator to Run mode. Then set the display format to i 3 and
key the limits of integration into the X- and Y-registers.
Keystrokes Display
|¥
Run mode.
´i 3
Sets display format to i 3.
0
v 0.000 00
Keys lower limit into Y-
register.
‛
99
1 99
Keys upper limit into X-
register.
´ f 1 0.000 00
Approximation of integral.
The answer returned by the calculator is clearly incorrect, since the actual
integral of f(x) = xe
-x
from 0 to

is exactly 1. But the problem is not that
you represented

by 10
99
since the actual integral of this function from 0 to
10
99
is very close to 1. The reason you got an incorrect answer becomes
apparent if you look at the graph of f(x) over the interval of integration: