100  REM*****CRVLEN***** MATH PROGRAM
110  DIM Q$(9)
120  PRINT TAB(20);"LENGTH OF CURVE"
121  PRINT 
122 INPUT "DO YOU WANT INSRUCTIONS";I$:IF ASCII(I$)=78% THEN PRINT:
	PRINT "IT IS ASSUMED THAT YOU HAVE ENTERED YOUR FUNCTION":
	PRINT "IN LINE 300":GO TO 200
125  PRINT " THIS PROGRAM APPROXIMATES THE LENGTH OF ANY CURVE BETWEEN"
126  PRINT "TWO POINTS HAVING P AND Q AS THEIR RESPECTIVE ABSCISSAS."
127  PRINT " THE PROGRAM DIVIDES THE CURVE INTO INCRESING NUMBERS OF"
128  PRINT "SUB INTERVA, JOINS THESE WITH SECANTS AND FINDS THE SUM"
129  PRINT "OF THESE SECANTS."
130  PRINT 
131  PRINT " TO INPUT THE FUNCTION WHICH YOUR CURVE REPRESENTS, TYPE AS"
132  PRINT " FOLLOWS AFTER THE PROGRAM STOPS:"
133  PRINT 
135  PRINT "           300 DEF FNY(X)=...(YOUR FUNCTION OF X)..."
137  PRINT 
140  PRINT "FOR EXAMPLE TO USE THE FUNCTION 2*X^3+3*X^2-2*X+3"
141  PRINT " YOU WOULD TYPE:"
142  PRINT 
144  PRINT "           300 DEF FNY(X)=2*X^3+3*X^2-2*X+3"
146  PRINT 
150  STOP 
200  PRINTWHAT ARE THE ABSCISSAS OF THE END POINTS OF THE INTERVAL"
201  PRINT "WHOSE LENGTH YOU WANT (SMALLER ONE FIRST: P,Q)";
207  INPUT P,Q
208  IF P<Q THEN 213
209  PRINT " P MUST BE LESS THAN Q!"
210  GOTO 207
213  PRINT 
214  PRINT " NUMBER OF","    SUM OF"
215  PRINT "SUBINTERVALS","SECANT LENGTHS";"  % CHANGE IN LENGTH"
216  PRINT "------------","--------------";"  ------------------"
217  PRINT 
230  S1=0
251  FOR N=1 TO 9
300  DEF FNY(X)=2*X^3+3*X^2-2*X+3
310  E=2^(N-1)
320  H=(Q-P)/E
3  S=0
340  FOR I=0 TO E-1
350  L=SQR((FNY(P+I*H+H)-FNY(P+I*H))^2+H*H)
360  S=S+L
362  NEXT I
364  IF S1>0 THEN 370
366  PRINT E,S,"  NO PREVIOUS VALUE"
368  GOTO 390
370  P5=((ABS(S1-S))/S1)*100
380  PRINT E,S,"  "P5
390  S1=S
395  NEXT N
400  PRINT 
401  PRINT "*****"
402  PRINT 
403  PRINT "WOULD YOU LIKE TO TRY NEW END POINTS";
404  INPUT Q$
405  IF Q$="YES" THEN 210
406  PRINT 
410 PRINT "TO TRY ANOTHER FUNCTION RETYPE LINE 300 AND THEN RUN"
500  END