simpson3by8.cpp

#include<vector>
#include<cmath>
#include<iomanip>

using namespace std;

double func(vector<double> poly, double x,int degree,double exp)
{
 for(int i=0; i<degree; i++)
 {
   exp += ((poly.at(i))*(pow(x,(degree-i-1))));
 }
 return exp;
}

int main()
{
 char y;
 do
 {

  int degree;
  double exp=0.0,x,n,a,b,temp;
  double val=0;
  double h,x2, segments,answer=0;
  vector<double> poly;
  cout<<"Enter the degree of polynomial\n";
  cin>>degree;
  degree++;
  cout<<"Enter coefficient\n";
    while(poly.size()<degree)  // input the coefficients
    {
     cin>>n;
     poly.push_back(n);
   }
   for(int i=0; i<degree;i++)   //  display the equation
   {
    if(i!= (degree-1))
      cout<<poly.at(i)<<"x^"<<(degree-i-1)<<" + ";
    else
      cout<<poly.at(i)<<endl;
  }

  cout<<"enter the limits and number of segments \n";
  cin>>a>>b>>segments;
  h= (b-a)/segments;
  cout<<"The value of h is : "<<h<<endl;
  cout<<"Value at a is : "<<func(poly, a, degree, exp)<<endl;
  cout<<"Value at b is : "<<func(poly, b, degree, exp)<<endl;

  answer += func(poly, a, degree, exp) + func(poly, b, degree, exp);
  
  if (segments > 0)
  {

    for (int i = 1; i <= segments-1; ++i)
    {
      val += h;
      if (i%3 == 0)
      {
        answer += 2*func(poly, val, degree, exp);
      }
      else
        answer += 3*func(poly, val, degree, exp);
    }
  }
  answer *= (3*h)/8;
  cout<<"Final answer is  : "<<answer<<endl;
  cout<<"Want to solve more equations\n Press 'y' or 'Y' for yes and any other key for no\n";
  cin>>y;
}while(y=='y' || y=='Y');
}