C# で 積分(台形則)して π を求める

πの求め方

積分(台形則)

using System;

public class CS0601
{
    public static void Main()
    {
        const double a = 0;
        const double b = 1;

        // 台形則で積分
        int n = 2;
        for (int j = 1; j <= 10; j++)
        {
            double h = (b - a) / n;  
            double s = 0;
            double x = a;
            for (int i = 1; i <= n - 1; i++)
            {
                x += h;
                s += f(x);
            }
            s = h * ((f(a) + f(b)) / 2 + s);
            n *= 2;

            // 結果を π と比較
            Console.WriteLine(string.Format("{0,2:D} : {1,13:F10}, {2,13:F10}", j, s, s - Math.PI));
        }
    }

    private static double f(double x)
    {
        return 4 / (1 + x * x);
    }
}

Z:\>csc -nologo CS0601.cs

Z:\>CS0601
 1 :  3.1000000000, -0.0415926536
 2 :  3.1311764706, -0.0104161830
 3 :  3.1389884945, -0.0026041591
 4 :  3.1409416120, -0.0006510415
 5 :  3.1414298932, -0.0001627604
 6 :  3.1415519635, -0.0000406901
 7 :  3.1415824811, -0.0000101725
 8 :  3.1415901105, -0.0000025431
 9 :  3.1415920178, -0.0000006358
10 :  3.1415924946, -0.0000001589

参考文献