# Numerical Integration using Monte Carlo method # FB - 201006137 import math import random # define any function here! def f(x): return math.sin(x) # define any xmin-xmax interval here! (xmin < xmax) xmin = 0.0 xmax = 2.0 * math.pi # find ymin-ymax numSteps = 1000000 # bigger the better but slower! ymin = f(xmin) ymax = ymin for i in range(numSteps): x = xmin + (xmax - xmin) * float(i) / numSteps y = f(x) if y < ymin: ymin = y if y > ymax: ymax = y # Monte Carlo rectArea = (xmax - xmin) * (ymax - ymin) numPoints = 1000000 # bigger the better but slower! ctr = 0 for j in range(numPoints): x = xmin + (xmax - xmin) * random.random() y = ymin + (ymax - ymin) * random.random() if math.fabs(y) <= math.fabs(f(x)): # area over x-axis is positive, and under is negative ctr += math.copysign(1, y) fnArea = rectArea * float(ctr) / numPoints print "Numerical integration = " + str(fnArea)