数值积分之Simpson 3/8法则

//实现Simpson 3/8法则

#include <iostream>

#include <math.h>

using namespace std;

class simpson2

{

private:

int n, k;

double a, b, f, integral, interval, one_third_interval;

double sum_term1, sum_term2, sum_term3, x;

public:

double func(double x)

{

f = (5.093e-5 * exp(2 * x)) / pow((1 + x * x), 2);

return f;

}

void integration();

};

void main()

{

simpson2 simp2;

simp2.integration();

}

void simpson2::integration()

{

cout << "\n输入上限和下限：";

cin >> b >> a;

cout << endl << "\n输入你要使用simpson 3/8法则的数目（即等分数）：";

cin >> n;

interval = (b - a) / n;

one_third_interval = interval / 3.0;

sum_term1 = 0.0;

sum_term2 = 0.0;

sum_term3 = 0.0;

for (k = 1; k < n; k++)

{

x = a + k * interval;

sum_term1 += func(x);

sum_term2 += func(x + one_third_interval);

sum_term3 += func(x + 2 * one_third_interval);

}

integral = (2 * sum_term1 + 3 * sum_term2 + 3 * sum_term3 - func(a) + func(b)) * (3 * one_third_interval / 8);

cout << endl << "积分值 = " << integral << endl;

}