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 = -3.05614388902526E-05
expect = -3.05614388888252E-05
relative error = -4.67047941622356E-11
relative error estimate = 1.04883755414239E-08
Link to C# source.