100 DEFDBL A-H, O-Z 105 DEF FNA (x AS DOUBLE) = SQR(1! + COS(x) * COS(x)) 110 A = 0!: REM This is the lower endpoint of [a,b]. 120 B = 4! * ATN(1!): REM This is the upper endpoint of [a,b]. 130 SUM = 0!: REM This is an accumulator. 135 REM The user is asked for a number of intervals, n, even and > 0. 140 INPUT "Enter number of intervals (must be even) "; N 145 IF N <= 0 OR (2 * FIX(N / 2) - N < 0) THEN PRINT "Input error": GOTO 140 150 H = (B - A) / N: REM The sub-interval size h = (b-a)/n. 160 FOR I = 1 TO N STEP 2: REM The "FOR" loop is done n/2 times. 170 SUM = SUM + FNA(A + (I - 1) * H) 175 REM: PRINT A + (I - 1) * H, FNA(A + (I - 1) * H) 180 SUM = SUM + 4! * FNA(A + I * H) 185 REM: PRINT A + I * H, FNA(A + I * H) 190 SUM = SUM + FNA(A + (I + 1) * H) 195 REM: PRINT A + (I + 1) * H, FNA(A + (I + 1) * H) 200 NEXT I: REM After loop, the sum is y_0+4*y_1+2*y_2+...+4*y_{n-1}+y_n. 210 PRINT "Sum = "; SUM: PRINT " Value of integral = "; SUM * H / 3 220 REM This short program will integrate a function FNA(x) from x = a to b. 230 PRINT "Theoretical value approximately "; 2 * SQR(2) * 1.35064388#