HP 33s - Manual (Page 124)

8–2 Integrating Equations
Integrating Equations (
³
FN)
To integrate an equation:
1. If the equation that defines the integrand's function isn't stored in the equation
list, key it in (see "Entering Equations into the Equation List" in chapter 6) and
leave Equation mode. The equation usually contains just an expression.
2. Enter the limits of integration: key in the lower limit and press ‘ , then
key in the upper limit.
3. Display the equation: Press | H and, if necessary, scroll through the
equation list (press ™ or š ) to display the desired equation.
4. Select the variable of integration: Press |  variable. This starts the
calculation.
 uses far more memory than any other operation in the calculator. If executing
 causes a  & " message, refer to appendix B.
You can halt a running integration calculation by pressing ‡ or g . However,
no information about the integration is available until the calculation finishes
normally.
The display format setting affects the level of accuracy assumed for your function
and used for the result. The integration is more precise but takes much longer in the
{} and higher {%}, { }, and {} settings. The uncertainty of the result
ends up in the Y–register, pushing the limits of integration up into the T– and
Z–registers. For more information, see "Accuracy of Integration" later in this
chapter.
To integrate the same equation with different information:
If you use the same limits of integration, press move them into the X– and
Y–registers. Then start at step 3 in the above list. If you want to use different limits,
begin at step 2.
To work another problem using a different equation, start over from step 1 with an
equation that defines the integrand.
Example: Bessel Function.
The Bessel function of the first kind of order 0 can be expressed as
³
=
π
π
dt t x x J
0
0
) sin cos(
1
) (