from math import*
import matplotlib.pyplot as plt
import numpy as np
pas=0.001
x=np.arange(1,2+pas,pas)
y=1/x
L=len(x)
int=0
for i in range(L-1):
  int=int+(y[i]+y[i+1])*(x[i+1]-x[i])/2
print(int)
print(log(2))
plt.plot(x,y,'x',markersize=4)
plt.show()