from numpy import *

def midtpunkt_metoden(f,a,b,n):
    h = (b-a)/float(n)
    
    s = 0;
    for i in range(1,n+1):
        s += f(a + (i-0.5)*h)
    s = h*s;
    return s;

def trapes_metoden(f,a,b,n):
    h = (b-a)/float(n)

    s = h * (f(a)+f(b))/2.0;
    
    for i in range(1,n):
        s += f(a + i*h)
    s = h*s;
    return s;
    

I = exp(1) - 1
f = lambda x: exp(x)
a = 0
b = 1
n = int(round(1e5*sqrt(exp(1)))/sqrt(12) +1)
print 'n: %d' % (n)

I_mid = midtpunkt_metoden(f, a, b, n)
I_trap = midtpunkt_metoden(f, a, b, n)

abserr_mid  = abs(I-I_mid)
abserr_trap = abs(I-I_trap)

print "|I - I_mid|: %g" % (abserr_mid)
print "|I - I_trap|: %g" % (abserr_trap)