from numpy import *


def midpoint(f, a, b, n):
	"""
	f - function
	a - start point of interval
	b - end point of interval
	n - number of subintervals
	"""
	h = (b-a)/n;
	s = 0;
	for i in range(1,n+1):
		xi_12 = a + (i-0.5)*h;
		s += f(xi_12);
	s = s*h;
	return s;
	
	
if __name__ == "__main__":
	# Ex 12.2.4 
	s = midpoint(exp, a=0, b=1, n=10);
	n = int(1/sqrt(24*1e-10/exp(1)))+1;
	s = midpoint(exp, 0,1,n);
	print("Midpoint: %g" % (s));
	print("Exact:    %g" % (exp(1)-1));