public class Integral    {        /// <summary>        /// 梯形公式        /// </summary>        /// <param name="fun">被积函数</param>        /// <param name="up">积分上限</param>        /// <param name="down">积分下限</param>        /// <returns>积分值</returns>        public static double TiXing(Func<double, double> fun, double up, double down)        {            return (up - down) / 2 * (fun(up) + fun(down));        }        /// <summary>        /// 辛普森公式        /// </summary>        /// <param name="fun">被积函数</param>        /// <param name="up">积分上限</param>        /// <param name="down">积分下限</param>        /// <returns>积分值</returns>        public static double Simpson(Func<double, double> fun, double up, double down)        {            return (up - down) / 6 * (fun(up) + fun(down) + 4 * fun((up + down) / 2));        }        /// <summary>        /// 科特克斯公式        /// </summary>        /// <param name="fun">被积函数</param>        /// <param name="up">积分上限</param>        /// <param name="down">积分下限</param>        /// <returns>积分值</returns>        public static double Cotes(Func<double, double> fun, double up, double down)        {            double C = (up - down) / 90 * (7 * fun(up) + 7 * fun(down) + 32 * fun((up + 3 * down) / 4)                     + 12 * fun((up + down) / 2) + 32 * fun((3 * up + down) / 4));            return C;        }              /// <summary>        /// 复化梯形公式        /// </summary>        /// <param name="fun">被积函数</param>        /// <param name="N">区间划分快数</param>        /// <param name="up">积分上限</param>        /// <param name="down">积分下限</param>        /// <returns>积分值</returns>        public static double FuHuaTiXing(Func<double, double> fun, int N, double up, double down)        {            double h = (up - down) / N;            double result = 0;            double x = down;            for (int i = 0; i < N - 1; i++)            {                x += h;                result += fun(x);            }            result = (fun(up) + result * 2 + fun(down)) * h / 2;            return result;        }        /// <summary>        /// 复化辛浦生公式        /// </summary>        /// <param name="fun">被积函数</param>        /// <param name="N">区间划分快数</param>        /// <param name="up">积分上限</param>        /// <param name="down">积分下限</param>        /// <returns>积分值</returns>        public static double FSimpson(Func<double, double> fun, int N, double up, double down)        {            double h = (up - down) / N;            double result = 0;            for (int n = 0; n < N; n++)            {                result += h / 6 * (fun(down) + 4 * fun(down + h / 2) + fun(down + h));                down += h;            }            return result;        }        /// <summary>        /// 复化科特斯公式        /// </summary>        /// <param name="fun">被积函数</param>        /// <param name="N">区间划分快数</param>        /// <param name="up">积分上限</param>        /// <param name="down">积分下限</param>        /// <returns>积分值</returns>        public static double FCotes(Func<double, double> fun, int N, double up, double down)        {            double h = (up - down) / N;            double result = 0;            for (int n = 0; n < N; n++)            {                result += h / 90 * (7 * fun(down) + 32 * fun(down + h / 4) + 12 * fun(down + h / 2) +                        32 * fun(down + 3 * h / 4) + 7 * fun(down + h));                down += h;            }            return result;        }        /// <summary>        /// 龙贝格算法        /// </summary>        /// <param name="fun">被积函数</param>        /// <param name="e">结果精度</param>        /// <param name="up">积分上限</param>        /// <param name="down">积分下限</param>        /// <returns>积分值</returns>        public static double Romberg(Func<double, double> fun, double e, double up, double down)        {            double R1 = 0, R2 = 0;            int k = 0; //2的k次方即为N（划分的子区间数）            R1 = (64 * C(fun, 2 * (int)Math.Pow(2, k), up, down) - C(fun, (int)Math.Pow(2, k++), up, down)) / 63;            R2 = (64 * C(fun, 2 * (int)Math.Pow(2, k), up, down) - C(fun, (int)Math.Pow(2, k++), up, down)) / 63;            while (Math.Abs(R2 - R1) > e)            {                R1 = R2;                R2 = (64 * C(fun, 2 * (int)Math.Pow(2, k), up, down) - C(fun, (int)Math.Pow(2, k++), up, down)) / 63;            }            return R2;        }        private static double S(Func<double, double> fun, int N, double up, double down)        {            return (4 * FuHuaTiXing(fun, 2 * N, up, down) - FuHuaTiXing(fun, N, up, down)) / 3;        }        private static double C(Func<double, double> fun, int N, double up, double down)        {            return (16 * S(fun, 2 * N, up, down) - S(fun, N, up, down)) / 15;        }    }