#!/usr/bin/python -Wall

# ----------------------------------------------------------------
# John Kerl
# kerl.john.r@gmail.com
# 2005-01-11
#
# This is an example of numerical integration in one variable: sin(x)/x from -2
# pi to 2 pi.  A reference value for the integral is 2.83630; this program
# prints 2.836350.
# ----------------------------------------------------------------
# This software is released under the terms of the GNU GPL.
# Please see LICENSE.txt in the same directory as this file.
# ================================================================

from __future__ import division # 1/2 = 0.5, not 0.
from math import *
import sys

# ----------------------------------------------------------------
# Integrand
def f(x):
	if (x == 0.0):
		return 1.0
	else:
		return sin(x) / x

# ----------------------------------------------------------------
xlo = -2.0 * pi
xhi =  2.0 * pi

argc = len(sys.argv)
nx  = 400
if (argc == 2):
	nx = float(argv[1])
dx  = (xhi - xlo) / nx

# Alternatively:
#dx  = 0.001

sum = 0.0
for k in range(0, nx):
	x = k * dx
	y = f(x)
	sum += y * dx
print "%11.6f" % (sum)