Example 3: Integral of the entire real line
The integral is computed and compared to its expected value. This integral is evaluated in Gradshteyn and Ryzhik (equation 3.417.1).
using System;
using Imsl.Math;
public class QuadratureEx3 : Quadrature.IFunction
{
public double F(double x)
{
return x / (4.0 * Math.Exp(x) + 9.0 * Math.Exp(-x));
}
public static void Main(String[] args)
{
Quadrature q = new Quadrature();
Quadrature.IFunction fcn = new QuadratureEx3();
double result = q.Eval(fcn, Double.NegativeInfinity,
Double.PositiveInfinity);
double expect = System.Math.PI * System.Math.Log(1.5) / 12.0;
Console.Out.WriteLine("result = " + result);
Console.Out.WriteLine("expect = " + expect);
}
}
Output
result = 0.106150517076628
expect = 0.106150517076633
Link to C# source.
Reference
Gradshteyn, I. S. and I. M. Ryzhik (1965), Table of Integrals, Series, and Products
, Academic Press, New York.