y=kwadratura('cos')\

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

double funkcja(double x){
    return cos(x);
}

int main(){
double x[5]={-0.906179845938664,-0.538469310105683,0,0.538469310105683,0.906179845938664};
double A[5]={0.236926885056189,0.478628670499366,0.568888888888889,0.478628670499366,0.236926885056189};
//y=A*feval(f,x)';
double wynik = 0;
for(int i = 0; i < 5; i++)
    wynik += A[i] * funkcja(x[i]);
cout <<" dla podanych danych \n x  =[-0.906179845938664,-0.538469310105683,0,0.538469310105683,0.906179845938664];\n A  =[0.236926885056189,0.478628670499366,0.568888888888889,0.478628670499366,0.236926885056189];\n"<<endl;
cout <<"********************************************" << endl<<endl<< "WYNIK: " <<wynik<<endl;
}




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


int main(){
double x[5]={-0.906179845938664,-0.538469310105683,0,0.538469310105683,0.906179845938664};
double A[5]={0.236926885056189,0.478628670499366,0.568888888888889,0.478628670499366,0.236926885056189};
//y=A*feval(f,x)';
double wynik = 0;
for(int i = 0; i < 5; i++)
    wynik += A[i] * cos(x[i]);

cout << wynik;
}






https://deepanshubhatti.blogspot.com/2013/10/to-evaluate-definite-integral-by-gauss.html

#include<iostream>
#include<cmath>
#include<iomanip>

using namespace std;


long double f(long double x)
{
    long double d;
    d=pow(x,3);
    return d;
}

//For Legendre's Polynomial Pn(x)
long double pn(long double a[],int n,int m,long double x)
{
    int i;
    long double p=0;
    if(m==0)
    {
        for(i=0;i<=n;i=i+2)
        {
            if(x==0)
                break;
            p+=a[i]*pow(x,i);
        }
    }
    else
    {
        for(i=1;i<=n;i=i+2)
        {
            p+=a[i]*pow(x,i);
        }
    }
    return p;
}

//Derivative of Pn(x)
long double dn(long double a[],int n,int m,long double x)
{
    int i;
    long double p=0;
    if(m==0)
    {
        for(i=0;i<=n;i=i+2)
        {
            if(x==0)
                break;
            p+=i*a[i]*pow(x,i-1);
        }
    }
    else
    {
        for(i=1;i<=n;i=i+2)
        {
            p+=i*a[i]*pow(x,i-1);
        }
    }
    return p;
}

//Factorial Function
long double fact(int n)
{
    int i;
    long double f=1;
    for(i=2;i<=n;i++)
    {
        f*=i;
    }
    return f;
}

//Main Function
int main()
{
    int n,m,i,N;
    double c,d;
    cout<<"wpisz wartosc n dla Pn(x) : \n";
    cin>>n;
    cout<<"wpisz dolna granice a dla calki : \n";
    cin>>c;
    cout<<"wpisz gorna granice b dla calki : \n";
    cin>>d;

    if(n<=0)
        return 0;A C++ Program To evaluate a Definite Integral by Gauss Quadrature Formula.

    long double a[n],b,x,y[n],z[n],w[n],l,v,s,g=0,u[n];
    m=n%2;
    if(m==0)
    {
        N=n/2;
    }
    else
    {
        N=(n-1)/2;
    }

    for(i=0;i<=N;i++)
    {
        a[n-2*i]=(pow(-1,i)*fact(2*n-2*i))/(pow(2,n)*fact(i)*fact(n-i)*fact(n-2*i));
    }

    if(m==0)
    {
        cout<<"\nThe Legendre's Polynomial is : ";
        cout<<a[0];
        for(i=2;i<=n;i=i+2)
            cout<<" + ("<<setprecision(10)<< a[i]<<") X^"<<i;
    }
    else
    {
        cout<<"\nThe Legendre's Polynomial is : ";
        cout<<"("<<a[1]<<") X";
        for(i=3;i<=n;i=i+2)
            cout<<" + ("<<a[i]<<") X^"<<i;
    }A C++ Program To evaluate a Definite Integral by Gauss Quadrature Formula.
    cout<<endl;

    //Roots of Pn(x)
    for(i=0;i<n;i++)
    {
        z[i]=cos(3.14*(i+0.75)/(n+0.5));
        l=z[i];
        do
        {
            s=l-(pn(a,n,m,l)/dn(a,n,m,l));
            v=l;
            l=s;
        }
        while(fabs(l-v)>0.0000000000000001);

        y[i]=l;
        w[i]=2/((1-pow(l,2))*(dn(a,n,m,l)*dn(a,n,m,l)));
    }

    for(i=0;i<n;i++)
    {
        u[i]=((d-c)*y[i]/2)+(c+d)/2;
    }
    cout<<"Roots\t\t\t\t"<<"Weights\n";
    for(i=0;i<n;i++)
    {
        cout<<setprecision(15)<<y[i]<<"\t\t"<<setprecision(15)<<w[i]<<endl;
    }

    for(i=0;i<n;i++)
        g+=w[i]*f(u[i]);

    g=g*(d-c)/2;
    cout<<"The Value of Integration is = "<<setprecision(10)<<g<<endl;
    return 0;
}