Simson's Rules in c++

  

Solution in C++: 

///******Bismillahir-Rahmanir-Rahim******///

///AH Tonmoy

///Department of CSE,23rd batch

///Islamic University,Bangladesh

#include<bits/stdc++.h>

using namespace std;

double givenfuction( double x)

{

    double a=1/x;// a=f(x) given funtion

    return a;

}

int main()

{

    int n,i;

    double a,b,dx,sum=0,integral;

    cout<<"Enter the limits of integration ,a= ";

    cin>>a;

    cout<<"Final limit, b=";

    cin>>b;

    cout<<"Enter the no  of subintervals, n= ";

    cin>>n;

    double x[n+1],y[n+1];

    dx=(b-a)/n; // del x value

    for (i=0; i<=n; i++)

    {

        x[i]=a+i*dx;  //evaluate x0,x1,x2...xn and store them in x[i] array

        y[i]=givenfuction(x[i]);  // evaluate y0,y1,y2...yn and also store y[i] array

    }

    // 4 2 4 pattern equation

    // f(x)=dx/3.0(f(x0)+4f(x1)+2f(x2)+4f(x3)+..........f(4*x(n-1)+f(x(n)))

    for (i=1; i<n; i+=2)

    {

        sum=sum+4.0*y[i];                //loop to evaluate 4*(y1+y3+y5+...+yn-1)

    }

    for (i=2; i<n-1; i+=2)

    {

        sum=sum+2.0*y[i];                /*loop to evaluate 4*(y1+y3+y5+...+yn-1)+

                                        2*(y2+y4+y6+...+yn-2)*/

    }

    integral=dx/3.0*(y[0]+y[n]+sum);         //h/3*[y0+yn+4*(y1+y3+y5+...+yn-1)+2*(y2+y4+y6+...+yn-2)]

    cout<<"The definite integral value  is "<<integral<<endl;

    return 0;

}