[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 }

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