Trapezoidal Rule for the Evaluation of Definite Integrals in c++ language

  

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  function

    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++)

    {

        //loop to  and y0,...yn

        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

    }

    // f(x)=dx/2.0(f(x0)+2f(x1)+2f(x2)+2f(x3)+..........f(2*x(n-1)+f(x(n)))

    for (i=1; i<n; i++)          //loop to evaluate h*(y1+y2...+yn-1)

    {

        sum=sum+dx*y[i];

    }

    integral=dx/2.0*(y[0]+y[n])+sum;        //h/2*[y0+yn+2(y1+y2+y3+...yn-1)]

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

    return 0;

}