Monte Carlo 数值积分

            var amount = 0.0d;
            var hitTheTargetCount = 0.0d;
            var M = 2.0d;
            var rnd=new Random();
            for (int i = 0; i < 1000; i++)
            {
                var x = rnd.NextDouble() * Math.PI;
                var y = rnd.NextDouble() * M;
                //Console.WriteLine("x:{0},y:{1}", x, y);
                if (y <= Math.Sin(x))
                {
                    hitTheTargetCount++;
                }
                amount++;
            }

            var s = (hitTheTargetCount / amount) * M * Math.PI;
            Console.WriteLine(s);

以上代码针对 sin(x) 0-pi 进行积分

积分int( sqrt(1-x^2),0,1)

        private void button1_Click(object sender, EventArgs e)
        {
            var amount = 0.0d;
            var hitTheTargetCount = 0.0d;
            var M = 1.0d;
            var rnd=new Random();
            for (int i = 0; i < 10000; i++)
            {
                var x = rnd.NextDouble() * M;
                var y = rnd.NextDouble() * M;
                //Console.WriteLine("x:{0},y:{1}", x, y);
                if (y <= Math.Sqrt(1-Math.Pow(x,2)))
                {
                    hitTheTargetCount++;
                }
                amount++;
            }

            var s = (hitTheTargetCount / amount) * M * M;
            Console.WriteLine(s * 4);
        }

        private void button2_Click(object sender, EventArgs e)
        {
            Func<double, double> func = (x) => { return (Math.Sqrt( 1 - Math.Pow(x, 2))); };

            var n = 10000;
            double h = 1.0d / n;
            double sumx = 0;
            double sum = func(0.0);

            for (int i = 1; i < n; i++)
            {
                sumx += h;
                var factor = ((i % 2) == 1) ? 4 : 2;
                //Console.WriteLine(i +":" + factor +"," + sumx);
                sum += factor * func(sumx);
            }
            sum += func(1);
            var v = 4 * (sum * h) / 3;
            Console.WriteLine(v);
        }