Example 4: Integral of an oscillatory function

The integral of cos(ax ) for a = 10^4 is computed and compared to its expected value. Because the function is highly oscillatory, the quadrature rule is set to 6. The relative error tolerance is also set. 
using System;
using Imsl.Math;

public class QuadratureEx4 : Quadrature.IFunction
{
    private double a;
    
    public QuadratureEx4(double a)
    {
        this.a = a;
    }

    public double F(double x)
    {
        return Math.Cos(a * x);
    }

    public static void  Main(String[] args)
    {
        double a = 1.0e4;
        Quadrature.IFunction fcn = new QuadratureEx4(a);
        
        Quadrature q = new Quadrature();
        q.Rule = 6;
        q.RelativeError = 1e-10;
        double result = q.Eval(fcn, 0.0, 1.0);
        
        double expect = Math.Sin(a) / a;
        Console.Out.WriteLine("result = " + result);
        Console.Out.WriteLine("expect = " + expect);
        Console.Out.WriteLine
            ("relative error = " + (expect - result) / expect);
        Console.Out.WriteLine
            ("relative error estimate = " + q.ErrorEstimate);
    }
}

Output

result = -3.05614388902539E-05
expect = -3.05614388888252E-05
relative error = -4.67475872674725E-11
relative error estimate = 1.04883755430041E-08
Link to C# source.