write a program to integrate a function using Romberg integration method in c++.

write a program to integrate a function using Romberg integration method in c++.

CODE:

#include<iostream.h>

#include<conio.h>

#include<math.h>

float f(float x)

{

return(1/(1+x));

}

float in(float i1, float i2)

{

return(i2+(i2-i1)/3);

}

void main()

{

clrscr();

int a,b;

float h,sum[6];

cout<<"enter lower limit : ";

cin>>a;

cout<<"enter upper limit : ";

cin>>b;

h = b-a;

for(int i=1;i<=3;i++)

{

sum[i]= 0.0;

int n =pow(2,i);

h=n/2;

cout<<"\n n="<<n<<"\t h="<<h<<endl;

sum[i]=(f(a)+f(b))/2;

for(int j=1;j<n;j++)

{

sum[i]+=f(a+j*h);

}

sum[i]*=h;

cout<<"\n x\t y";

for(j=0;j<=n;j++)

{

cout<<endl<<a+j*h<<"/t"<<f(a+j*h);

}

cout<<"\n I(h/"<<pow(2,i-1)<<")="<<sum[i]<<endl;

}

for(i=1;i<=3;i++)

{

if(i!=3)

{

sum[i+3]= (sum[i],sum[i+1]);

cout<<"I(h/"<<pow(2,i-1)<<",h/"<<pow(2,i)<<")="<<sum[i+3]<<endl;

}

else

{

sum[i+3]= (sum[i+1],sum[i+2]);

cout<<"I(h,h/2,h/4)="<<sum[i+3]<<endl;

}

}

getch();

}

OUTPUT: