196 Section 14: Numerical Integration
Keystrokes Display
| ¥
Run mode.
0 v
0.0000
Key lower limit, 0, into Y-register.
| $
3.1416
Key upper limit, π, into X-register.
| R
3.1416
Specify Radians mode for
trigonometric functions.
Now you are ready to press ´ f 0 to calculate the integral. When you
do so, you’ll find that—just as with _—the calculator will not
display the result right away, as it does with other operations. The HP 15c
calculates integrals using a sophisticated iterative algorithm. Briefly, this
algorithm evaluates f (x), the function to be integrated, at many values of
x between the limits of integration. At each of these values, the calculator
evaluates the function by executing the subroutine you write for that
purpose. When the calculator must execute the subroutine many times—
as it does when you press f—you can’t expect any answer right away.
Most integrals will require less than 5 seconds, but some integrals will
require more time. Later on we’ll discuss how you can decrease the time
somewhat; but for now press ´ f 0 and take a break (or read ahead)
while the HP 15c takes care of the drudgery for you.
Keystrokes Display
´ f 0
2.4040
=
cos (sin θ) dθ.
In general, don’t forget to multiply the value of the integral by whatever
constants, if any, are outside the integral. In this particular problem, we
need to multiply the integral by 1/π to get J
0
(1):
Keystrokes Display
| $
3.1416
÷
0.7652
J
0
(1).
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