C++ Program of Simpson’s 3/8th Rule for the Evaluation of Definite Integrals

  
//Simpson's 3/8th Rule for Evaluation of Definite Integrals 
#include<iostream> 
#include<cmath> 
using namespace std; 
double f(double x) {     
    double a=1/(1+x*x);    //write the function whose definite integral is to be calcuated here     
    return a; 
} 
int main() {
    cout.precision(4);        //set the precision
    cout.setf(ios::fixed);
    int n,i;            //n is for subintervals and i is for loop
    double a,b,c,h,sum=0,integral;
    cout<<"\nEnter the limits of integration,\n\nInitial limit,a= ";
    cin>>a;
    cout<<"\nFinal limit, b=";  //get the limits of integration
    cin>>b;
    cout<<"\nEnter the no. of subintervals(IT SHOULD BE A MULTIPLE OF 3), \nn=";
    //get the no. of subintervals
    cin>>n;
    double x[n+1],y[n+1];
    h=(b-a)/n;     //get the width of the subintervals
    for (i=0;i<n+1;i++){                        //loop to evaluate x0,...xn and y0,...yn
        x[i]=a+i*h;                //and store them in arrays
        y[i]=f(x[i]);     
    }
    for (i=1;i<n;i++)     {
        if (i%3==0)
            sum=sum+2*y[I];
        else
            sum=sum+3*y[I];
    }
    integral=3*h/8*(y[0]+y[n]+sum);  //3h/8*[y0+yn+3*(y1+y2+y4+...)+2*(y3+y6+y9+...+)]
    cout<<"\nThe definite integral  is "<<integral<<"\n"<<endl;
    return 0;
}  

outpu simpson 38 c++ program

Explanation of the code:

[wpedon id="7041" align="center"]

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