HP 33s - Manual (Page 126)

8–4 Integrating Equations
Now calculate J
0
(3) with the same limits of integration. You must respecify the
limits of integration (0, π) since they were pushed off the stack by the subsequent
division by π.
Keys: Display: Description:
0 ‘ | N
)  Enters the limits of integration
(lower limit first).
| H
 1%º 1!22 Displays the current equation.
| 
³  G_ Prompts for the variable of
integration.
T %@
)
 Prompts for value of X.
3 g
! !
³ /
.
) 

x = 3. Starts integrating and
calculates the result for
³
π
0
) (t f .
| N q
.
)
 The final result for
J
0
(3).
Example: Sine Integral.
Certain problems in communications theory (for example, pulse transmission
through idealized networks) require calculating an integral (sometimes called the
sine
integral) of the form
dx
x
x
t S
t
i
)
sin
( ) (
0
³
=
Find Si (2).
Enter the expression that defines the integrand's function:
x
x sin
If the calculator attempted to evaluate this function at x = 0, the lower limit of
integration, an error (# &
) would result. However, the integration
algorithm normally does not evaluate functions at either limit of integration, unless
the endpoints of the interval of integration are extremely close together or the
number of sample points is extremely large.