[算法][求积分][复合辛普森公式]

 1 //这里f()为被积函数，输入a,b为积分上下限，
 2 //eps为计算精度[这里要注意假收敛，一般设小一点好]
 3 #include <iostream>
 4 #include <cmath>
 5 #define  eps 1e-6
 6 using namespace std;
 7 double f(double x){
 8     return sqrt(1+cos(x)*cos(x));
 9 }//被积函数
10 double Sn(double a,double b,double n){
11     double h=(a+b)/(2*n);
12     double sum=0;
13     for(int k=1;k<=n;k++){
14         sum+=2*f(a+(2*k-1)*h);
15         sum+=f(a+2*k*h);
16     }
17     sum=(sum*2+f(a)-f(b))*h/3;
18     return sum;
19 }//辛普森公式
20 double Solve(double a,double b){
21     int i=1;
22     double S1n=Sn(a,b,i);
23     double S2n=Sn(a,b,2*i);
24     while(fabs(S1n-S2n)>eps){
25         cout<<"n = "<<i<<"  S1 = "<<S1n<<"  S2 = "<<S2n<<‘\n‘;
26         i++;
27         S1n=S2n;
28         S2n=Sn(a,b,2*i);
29     }
30     return S2n;
31 }
32 int main(){
33     cout<<Solve(0,48)<<‘\n‘;
34 }