Интегрирование табличных функций

Интегрирование методом трапеций , для m равных отрезков:

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5 CLS

6 n0 = 5001: DIM p(n0)

10 INPUT " n = ", n

15 IF (n < = 0) OR (n > n0) THEN END

30 a = 0

40 b = 1

50 REM pi = 3.1415926

60 h0 = (b - a) / n

70 FOR i = 1 TO n

80 x = a + h0 * (i - 1)

90 p(i) = 2 * EXP(-x * x) / SQR(pi)

100 NEXT i

110 s = 0

120 FOR i = 1 TO n - 1

130 s = s +.5 * h0 * (p(i) + p(i + 1))

140 NEXT i

150 PRINT " Integral to tropezia = ", s

151 PRINT " Toch value = 0.8427008"

152 GOTO 10

160 END

Интегрирование методом Симпсона (парабол), для m равных отрезков:

5 CLS

6 REM ------------------------- SIMPSON -------------------------------------

10 a = 0

20 b = 1

30 INPUT " m = ", m

40 IF m < = 0 THEN END

50 h = (b - a) / m / 2: x = a

55 GOSUB 110: i = f: n = 0

60 x = x + h: GOSUB 110: i = i + 4 * f

70 n = n + 2: IF n = 2 * m THEN 90

80 x = x + h: GOSUB 110: i = i + 2 * f: GOTO 60

90 x = b: GOSUB 110: i = (i + f) * h / 3

100 PRINT " Integral to Simpson="; i: GOTO 30

110 f = SQR(2 * x + 1): RETURN

120 END

Точное значение Integ = 1, 398717.

Интегрирование методом Бодэ, для 5 равных отрезков длинною h:

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1 REM------------------ BODE01.BAS -----------------------

5 CLS

10 PRINT " Integral to Bode"

20 A = 0

30 B = 1

40 INPUT " M = ", M

45 IF M < = 0 THEN 140

46 x = A

50 H = (B - A) / M

51 E = H / 4

52 H = A

53 GOSUB 130: I = 7 * F

60 FOR N = 1 TO M

61 x = x + E

70 GOSUB 130: I = I + 32 * F: x = x + E

80 GOSUB 130: I = I + 12 * F: x = x + E

90 GOSUB 130: I = I + 32 * F: x = x + E

100 GOSUB 130: I = I + 14 * F

110 NEXT N

120 I = I - 7 * F: I = I * 2 * E / 45

125 PRINT " Integral = "; I: GOTO 40

130 F = SQR(2 * x + 1)

131 RETURN

140 END

Точное значение Integ = 1, 398717.