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11-6 Applications
This program uses Simpson’s method to estimate the definite integral of a
function.
Estimate the definite integral of
‰
0
1.5
(6
ì
6x
5
)dx
and graph the area of the integral.
The program estimates the definite integral for
Y1
using
Simpson’s method. It prompts for the lower and upper limits
of integration and the number of divisions.
PROGRAM:SIMPSON
:INPUT "LOWER LIMIT=",A
Input lower limit.
:INPUT "UPPER LIMIT=",B
Input upper limit.
:INPUT "N DIVISIONS=",D
Input # of divisions.
:0
→
S
Initialize sum variable.
:(B
ì
A)/(2
×
D)
→
W
Calculate division width.
:FOR(J,1,D,1)
Begin calculation loop.
:A+2(J
ì
1)W
→
L
Calculate left point.
:A+2JW
→
R
Calculate right point.
:(L+R)/2
→
M
Calculate midpoint.
:W(Y1(L)+4Y1(M)+Y1(R))
/3+S
→
S
Calculate division sum and
add to total.
:END
:DISP "AREA="
Display results.
:DISP S
Follow this procedure to solve the problem.
1. Enter the program.
2. Press
(
and enter the function in
Y1
. Turn any other
functions off.
Program: Numerical Integration
Problem
Program
Procedure