1 using System;
 2 using MathNet.Numerics.Integration;
 3 
 4 namespace MathNet.Numerics
 5 {
 6     /// <summary>
 7     /// 数值积分类
 8     /// </summary>
 9     public static class Integrate
10     {
11         /// <summary>      
12         /// 近似解析光滑函数在闭区间上的定积分
13         /// </summary>
14         /// <param name="f">The analytic smooth function to integrate.</param>
15         /// <param name="intervalBegin">Where the interval starts, inclusive and finite.</param>
16         /// <param name="intervalEnd">Where the interval stops, inclusive and finite.</param>
17         /// <param name="targetAbsoluteError">The expected relative accuracy of the approximation.</param>
18         /// <returns>Approximation of the finite integral in the given interval.</returns>
19         public static double OnClosedInterval(Func<double, double> f, double intervalBegin, double intervalEnd, double targetAbsoluteError)
20         {
21             return DoubleExponentialTransformation.Integrate(f, intervalBegin, intervalEnd, targetAbsoluteError);
22         }
23 
24         /// <summary>   
25         ///  近似解析光滑函数在闭区间上的定积分
26         /// </summary>
27         /// <param name="f">The analytic smooth function to integrate.</param>
28         /// <param name="intervalBegin">Where the interval starts, inclusive and finite.</param>
29         /// <param name="intervalEnd">Where the interval stops, inclusive and finite.</param>
30         /// <returns>Approximation of the finite integral in the given interval.</returns>
31         public static double OnClosedInterval(Func<double, double> f, double intervalBegin, double intervalEnd)
32         {
33             return DoubleExponentialTransformation.Integrate(f, intervalBegin, intervalEnd, 1e-8);
34         }
35     }
36 }

 1 // 1. Integrate x*x on interval [0, 10]
 2 Console.WriteLine(@"1.函数 x*x 在闭区间 [0, 10] 上的积分");
 3 var result = Integrate.OnClosedInterval(x => x * x, 0, 10);
 4 Console.WriteLine(result);
 5 Console.WriteLine();
 6 
 7 // 2. Integrate 1/(x^3 + 1) on interval [0, 1]
 8 Console.WriteLine(@"2.函数 1/(x^3 + 1) 在闭区间 [0, 1] 上的积分");
 9 result = Integrate.OnClosedInterval(x => 1 / (Math.Pow(x, 3) + 1), 0, 1);
10 Console.WriteLine(result);
11 Console.WriteLine();
12 
13 // 3. Integrate f(x) = exp(-x/5) (2 + sin(2 * x)) on [0, 10]
14 Console.WriteLine(@"3.函数 f(x) = exp(-x/5) (2 + sin(2 * x)) 在 [0, 10]上的积分");
15 result = Integrate.OnClosedInterval(x => Math.Exp(-x / 5) * (2 + Math.Sin(2 * x)), 0, 100);
16 Console.WriteLine(result);
17 Console.WriteLine();
18 
19 // 4. Integrate target function with absolute error = 1E-4
20 Console.WriteLine(@"4. 对目标函数进行积分，绝对误差= 1E-4 ,区间 [0, 10]");
21 Console.WriteLine(@"public static double TargetFunctionA(double x)
22 {
23 return Math.Exp(-x / 5) * (2 + Math.Sin(2 * x));
24 }");
25 result = Integrate.OnClosedInterval(TargetFunctionA, 0, 100, 1e-4);
26 Console.WriteLine(result);
27 Console.WriteLine();

1.函数 x*x 在闭区间 [0, 10] 上的积分
333.333333333332

2.函数 1/(x^3 + 1) 在闭区间 [0, 1] 上的积分
0.835648848264702

3.函数 f(x) = exp(-x/5) (2 + sin(2 * x)) 在 [0, 10]上的积分
10.4950494839272

4. 对目标函数进行积分，绝对误差= 1E-4 ,区间 [0, 10]
public static double TargetFunctionA(double x)
{
    return Math.Exp(-x / 5) * (2 + Math.Sin(2 * x));
}
10.4950494839276