gistfile1.py

import math
F = lambda x: 1/((1+math.sin(2*x))**2)
def rectangle_method(a, b, E, c):
    n = 2
    JN1 = 0
    while 1:
        h = (b - a)/n
        x = a + c*h
        S = 0
        for i in range(n):
            S = S+F(x)
            x = x+h
        JN = S*h
        if abs(JN-JN1)<=E:
            return n, JN
        else:
            n=2*n
            JN1 = JN

def trapezoidal_rule(a, b, E, c):
    n = 2
    JN1 = 0
    while 1:
        h = (b - a)/n
        x = a
        S = F(a) + F(b)
        for i in range(1,n):
            x = x+h
            S = S+2*F(x)
        JN = S*h/2
        if abs(JN-JN1)<=E:
            return n, JN
        else:
            n=2*n
            JN1 = JN

def simpsons_rule(a, b, n):
    h = (b - a) / n
    S = F(a)

    for i in range(1, n, 2):
        x = a + h * i
        S += 4 * F(x)

    for i in range(2, n-1, 2):
        x = a + h * i
        S += 2 * F(x)

    S += F(b)
    z = h * S / 3

    return z


print(rectangle_method(0, 2, 0.0001, 0))
print(trapezoidal_rule(0, 2, 0.0001, 0))
print(simpsons_rule(0, 2, 1000))