from  matplotlib import pyplot as plt

from math import exp, acos, log10

import numpy as np

​

#  function to integrate                                                                                     

def function(x):

    return 1.0/(1+x*x)

​

#  new probability                                                                                           

def newfunction(x):

    return 0.3333333*(4.0-2*x)

​

Dim = 100

x = np.linspace(0.0,1.0,Dim)

f = np.zeros(Dim)

g = np.zeros(Dim)

for i in xrange(Dim):

    f[i] = function(x[i])

    g[i] = newfunction(x[i])

​

plt.plot(x, f ,'b-',x, g,'g-')

plt.axis([0,1,0.5, 1.5])

plt.xlabel('$x$')

plt.ylabel('Functions')

plt.title('Similarities between functions')

plt.legend(['Integrand', 'New integrand'], loc='best')

plt.savefig('newprobability.pdf')

plt.show()