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simpson's 1/3 rule


 ///Bismillahir Rahmanir Rahim
///Author:Tanvir Ahmmad
///Dept.CSE,IU,Bangladesh




#include<iostream>
using namespace std;

int main()
{

    double up,low,h,arr_y[1009],sum=0;
    cout<<"Given function f(x)=1/(1+X)"<<endl<<"Given the upper limit of integration : ";
    cin>>up;
    cout<<"Given the lower limit of integration : ";
    cin>>low;
    cout<<"Given the value of h : ";
    cin>>h;
    int n=(up-low)/h;
    cout<<"So the value of n = "<<n<<endl;
    for(int i=0; i<=n; i++)
    {
        arr_y[i]=(1.0/(1.0+(i*h)));
        if(i==0) cout<<"X=X0        Y["<<i<<"]="<<arr_y[i]<<endl;
        else cout<<"X=X0+"<<i<<"h"<<"     Y["<<i<<"]="<<arr_y[i]<<endl;
    }
    for(int i=1;i<n;i++)
    {
        if(i%2==1)  sum+=(4*arr_y[i]);
        else sum+=(2*arr_y[i]);
    }
    sum+=(arr_y[0]+arr_y[n]);
    cout<<"Required value of integration is: "<<(sum*h)/3.0<<endl;
    return 0;

}



///Alhamdulillah


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