HP HP-11C - Numerical Integration by Discrete Points

Section 10: Applications Programs
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:
1569
Let x¢, x1, ..., X, be n + 1 equally spaced points (x; =x¢ +jh,j =0, 1,
2, ..., n) at which corresponding values f(x;), f(x) ..., f(x,) of the
function f(x) are known.
Xn
The integral: f f(x)dx may be approximated using:
x
1. Thetrapezoidal rule:
n-1
[ a2 o2 2 )+
Jj=1
2. Simpson’srule:
j;on f(x)dx ~% [f(xg) +4f(x;) +2f(xg) + ... 4f(x,,_3)
+ 2f(xn-2) + 4f(xn,-1) +f(xn)]
In order to apply Simpson’s rule, n must be even. If it is not, Error O
will be displayed.
KEYSTROKES DISPLAY KEYSTROKES DISPLAY
(fJCLEAR [PRGM] |000- (sT0]O 005- 44 O
001-42,21,11|(5T0)5 006- 44 5
(ST0)4 002- 44 4|0 007- 0
R/S 003- 31|[s70]3 008- 44 3
004-42,21,12 |[f)(LBL)1 009-42,21, 1