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196 Section 14: Numerical Integration

Keystrokes

Display

| ¥

Run mode.

0 v

0.0000

Key lower limit, 0, into Y-

| $

3.1416

-

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 on the order of 2 to 10 seconds; but some integrals

will require even more. 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





dθ θ)(sin cos

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 t to get J

(1):

Keystrokes

Display

3.1416

0.7652

(1).

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HP 15C Bedienungsanleitung Seite 196