baluev_3.2

import sys, math, random, ROOT

input_x_a = 0.01
input_x_b = 1
input_y_a = 0
input_y_b = 1

def f(x,y):
    # return math.exp(x + y)/(1 + math.sqrt(x)*y/2)
    return 1 / ( math.pow(x,2) * ( y + math.sin(x)/2 ) )

def f(x, y):
    return g1(x, y) + g2(x, y)
def g1(x, y):
    return 6.5 * y
def g2(x, y):
    return -6.5 * y + math.exp(x + y)/(1 + math.sqrt(x)*y/2)

g1_int = 6.5 * (input_x_b - input_x_a) * (input_y_b / 2 - input_y_a / 2)

def single(f, x_limits, y_limits):
    x_a, x_b = x_limits
    y_a, y_b = y_limits
    x = ROOT.gRandom.Uniform(x_a, x_b)
    y = ROOT.gRandom.Uniform(y_a, y_b)
    return (x_b - x_a) * (y_b - y_a) * f(x, y)

results = []
for i in range(10):
    cresults = []
    for i in range(1000):
        r = (single(g2, (0., 0.5), (1., 3.)))
        results.append(r)
        cresults.append(r)
    average = sum(results) / len(results)
    variance = (sum(r**2 for r in results) - average**2) / len(results)
    caverage = sum(cresults) / len(cresults)
    cvariance = (sum(r**2 for r in cresults) - caverage**2) / len(cresults)
    print g1_int + caverage, math.sqrt(cvariance / len(cresults)),
    print g1_int + average, math.sqrt(variance / len(results))

def f_for_drawing(x, p):
    return g2(x[0], x[1])

tf2 = ROOT.TF2("f", f_for_drawing, 0., 0.5, 1., 3., 1)
tf2.Draw("surf1z")
sys.stdin.readline()