numerical_int.py

    from math import e, pi, sqrt

    def get_xvalues(a,b,N):
        dist = 1.0*b - 1.0*a
        dx = dist/N
        half = dx/2.0
        R = [(a + dx * n + half) for n in range(N)]
        return R, dx

    def integrate(a,b,f,N=100):
        '''integrate function f over [a,b]'''
        L, dx = get_xvalues(a,b,N)
        values = [f(x) for x in L]
        print sum(values) * dx

    def f(x):
        return x**2

    integrate(0,1,f)
    integrate(1,2,f)

    def g(x):
        exp = -0.5*x**2
        norm = sqrt(2*pi)
        return e**(exp) / norm

    for b in [2,4,6,8,10]:
        print str(b).rjust(2),
        integrate(-b,b,g)