Numerical Integration By Discrete Points - HP -11C Owner's Handbook Manual

188 Section 10: Applications Programs
For new tolerances go to stap 8.
For a naw f(x) go to the end of the
program
Set program made and delete lines
068-42,21,13 back to (CBL)[C)
Go to step 4.
Example: Find a root of
f(x) =x8~x-1=0
with xo =
Keystrokes Display
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9 |[P/R 068-42,21,13
5
05 (1 075- 30
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Set User mode.
(4) 0.000000010 Default cand Ax.
2 (8) 1.134724138 x;
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Section 10: Applications Programs 169
Numerical Integration by Discrete Points
This program will perform numerical integration when a function
is known at a finite number of equally spaced points (discrete case).
The integrals are approximated by either the trapezoidal rule or
Simpson's rule.
Equations:
Let x9, 21, ...,, ben + | equally spaced points (x; = x9 +jh,j=0,1,
2, ..., n) at which corresponding values f(xp), f(x) ..., f(x,) of the
function f(x) are known.
nr
The integral: yp f(x)dx may be approximated using:
0
1. The trapezoidal rule:
Xp =
f fixyds~*
f(xo) +2 se f(x) } + f(x)
yl
2. Simpson's rule:
tn
LP rays ~* tx) +44 a) + 2f la) + Alin)
+ 2f(Xp-2) + 4F(Xn-1) + f(%p))
In order to apply Simpson's rule, n must be even. If it is not, Error 0
will be displayed.
KEYSTROKES [DISPLAY | _EVSTRONES | SPLAT _|
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001-42,21,11 | [STO
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