HP 15c - Manual (Page 44)

44 Section 2: Working with f
44
4. To get the integral over the entire interval of integration, add together the
approximations and their uncertainties from the integrals calculated over each
subinterval. You can do this easily using the z key.
Before subdividing the integration, check whether the calculator underflows when evaluating
the function around the upper (or lower) limit of integration.
‡
Since there is no reason to
evaluate the function at values of x for which the calculator underflows, in some cases the
upper limit of integration can be reduced, saving considerable calculation time.
Remember that once you have keyed in the subroutine that evaluates f(x), you can calculate
f(x) for any value of x by keying that value into the X-register and pressing
vvvG followed by the label of the subroutine.
If the calculator underflows at the upper limit of integration, try smaller numbers until you
get closer to the point where the calculator no longer underflows
For example, consider the approximation of



0
dx xe
x
.
Key in a subroutine that evaluates f(x) = xe
−x
.
Keystrokes Display
|¥
Program mode.
´CLEARM 000- Clears program memory.
´b1 001-42,21, 1
” 002- 16
' 003- 12
* 004- 20
|n 005- 43 32
Set the calculator to Run mode and set the display format to i3. They try several values
of x to find where the calculator underflows for your function.
Keystrokes Display
|¥
Run mode.
´i3
Sets format to i3.
“3 1 03 Keys 1000 into X-register
vvv 1.000 03 Fills the stack with x.
G1 0.000 00 Calculator underflows at x =
1000.
300
v 3.000 02
G1 0.000 00 Calculator still underflows.
‡
When the calculation of any quantity would result in a number less than 10
−99
, the result is replaced by zero. This
condition is known as underflow.