CLS
PRINT "INTEGRAL EVALUATION BY MEANS OF "
PRINT "A MODIFIED SIMPSON METHOD"
PRINT
PRINT
INPUT "KEY IN LOWER LIMIT = ";A
INPUT "KEY IN UPPER LIMIT = ";B
[ONNIZE]
PRINT "TYPE 5 FOR A TOL OF 1E-5, ETC."
INPUT "KEY IN TOLERANCE (USE INTEGER)= ";E
E=1/10^E
M = (A+B)/2
H1 = (B-A)/40
GOSUB [THNIZE]
REM ==EVALUATE PRINCIPAL TERMS OF DEFINITE INTEGRAL==
N = ((B-A)^5*D/E/180)^.25
N = 2*INT(N/2+1)
S = 0
X = A
H = (B-A)/N
FOR I = 1 TO N/2
GOSUB [THSEZE]
S = S + F
X = X + H
GOSUB [THSEZE]
S = S + 4 * F
X = X + H
GOSUB [THSEZE]
S = S + F
NEXT I
PRINT
PRINT
ANS=S*H/3
PRINT "FOR A TOLERANCE OF "; E; " , ";" I("; N;")= ";ANS
PRINT
PRINT "DO YOU WANT A NEW TOLERANCE"
PRINT "(1 = YES,  0 = NO)  ";
INPUT " ";W
IF W = 1 THEN [ONNIZE]
GOTO [FOSEZE]
[THSEZE]
REM *******************************************
REM ==SUBROUTINE WHICH DEFINES USER FUNCTION=
F = X/(9+X*X)^.5
REM *******************************************
RETURN
REM ==SUBROUTINE TO EVALUATE ERROR==
[THNIZE]
D = 0
X = M -2 * H1
GOSUB [THSEZE]
D = D + F
X = M -H1
GOSUB [THSEZE]
D = D -4 * F
X = M
GOSUB [THSEZE]
D = D + 6 * F
X = M + H1
GOSUB [THSEZE]
D = D -4 * F
X = M + 2 * H1
GOSUB [THSEZE]
D = D + F
D = ABS(D)/H1^4
RETURN
[FOSEZE]
END