//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;
}

I'm a physicist specializing in theoretical, computational and experimental condensed matter physics. I like to develop Physics related apps and softwares from time to time. Can code in most of the popular languages. Like to share my knowledge in Physics and applications using this Blog and a YouTube channel.