HP 33s sinx, sin, )dx, 8–4, ￿ |Nq, Example: Sine Integral, 8–4 Integrating Equations

Now calculate J0(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:
￿ 0 ‘N	) 
H	 1%º 1!22
	≥  G_
T	%@
	)
3 g	!!
	≥ /
	.)
￿ Nq	.) 

Description:

Enters the limits of integration (lower limit first).

Displays the current equation. Prompts for the variable of integration.

Prompts for value of X.

x = 3. Starts integrating and calculates the result for

≥0π f (t ) .

The final result for

J0(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

Si	(t ) = ≥ t	(	sin x	)dx
	0		x

Find Si (2).

Enter the expression that defines the integrand's function:

sinx

x

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.

8–4Integrating Equations