Java で 積分(台形則)して π を求める

πの求め方

積分(台形則)

public class Java0601 {
    public static void main(String []args) {
        final double a = 0;
        final 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
            System.out.println(String.format("%2d : %13.10f, %13.10f", j, s, s - Math.PI));
        }
    }

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

Z:\>javac Java0601.java

Z:\>java Java0601
 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