复化梯形公式求积分

#include <iostream>
#include <cmath>
using namespace std;

double X[1000];//保存生成的节点横坐标
double Y[1000];//保存生成的节点纵坐标

//定义一个数学函数
double fun(double x)
{	
    return 4 / (1 + x * x);
}

//分割区间
void Devide(double a, double b, int N)
{	
    double x;	
    double dx= (b - a) / (N);	
    for (int i = 0; i <= N; i++)	
    {		
        x = a + i * dx;		
        X[i] = x;		
        Y[i] = fun(x);	
    }
}

//复化梯形求积
double GetIntegralValue(double a, double b, int N)
{	
    double sum = 0;	
    double value;	
    //求2*f(xk)的总和，1<= k <= n-1	
    for (int i = 1; i <= N - 1; i++)	
    {		
        sum += 2 * Y[i];
    }	
    value = 0.5 * ((b - a) / N) * (Y[0] + sum + Y[N]);	
    return value;
}

int main()
{	//产生的节点数	
    double a = 0;	
    double b = 1;	
    int N=10;	
    cout << "被积函数 f = 4 / (1 + x * x)" << endl;	
    cout << "区间等分数为 10" << endl;	
    cout << "积分区间为（0，1）" << endl;	
    Devide(a, b, N);	
    cout << "积分值为：" << GetIntegralValue(a, b, N) << endl;	
    return 0;
}

来源：https://blog.csdn.net/qq_43239560/article/details/101118528