?from math import *

def f(x):
	return cos(x)
	
def midpoint(f,a,b,n):
	h = (b-a)/n
	Int = 0.0
	x = a + 0.5*h
	for k in range(1,n+1):
		Int += f(x)
		x += h
	return (h*Int)
	

a = 0.0; b = 1.0
M = 30; eps = 1.0e-14

j = 1; n = 1
I = midpoint(f,a,b,n)
abserr = abs(I)

print ("%2i. iterasjon: I=%1.14f, relativ feil=%e"
  %(j, I, abserr/abs(I)))

while j<M and abserr>eps*abs(I):
	n = 2*n; j = j + 1
	Ip = I
	I = midpoint(f,a,b,n)
	abserr = abs(I-Ip)
	
	print ("%2i. iterasjon: I=%1.14f, relativ feil=%e"
	   %(j, I, abserr/abs(I)))
	
print ("\nEksakt verdi=%1.14f, eksakt relativ feil=%e"
   %(sin(1.0),abs(sin(1.0)-I)/abs(sin(1.0))))