# Calculate integral using analytically and Simpson methods

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Reputation: 0
• Posts: 4
• Joined: 06-December 12

# Calculate integral using analytically and Simpson methods

Posted 06 December 2012 - 04:27 AM

Hello,
I have problem with my program. I am trying to calculate analytically the value of integral with two different set of parameters
a) a=1 b=2 p=1-10^{-n} n=1,..,20
a=1 b=1+10^n p=0.5 n=1,..,20

and then for both I calculate the value using Simpson rule.

I don't know how to modify my code to calculate a) with Simpson rule, because now all the results are the same n and I don't know why after n=15 all my results are 0.

I was reading about double representation and I was analysing the Simpson rule and my analytically code for integral but I can't figure it out why there are 0, because I calculate it with Mathematica to improve my results and it gives
my some numbers not 0.

For now I have this code, the results from section and analytically from a) are ok expect n>15 where I have 0.
```#include <iomanip>
#include <iostream>
#include <cmath>
#include <fstream>

using namespace std;
const int N = 1;

double f(double x)
{
double dx, b=2.0, z, p;
int n;
for(n=1;n<=20;n++){
p=1 - (pow(10.0, (-n)));
z=1/(pow(x, p));
return z;}
}

double fx(double x)
{
double n;
double p=0.5;
double b=1 + (pow(10.0, (-n)));
double dx=(b-1)/N;
double z=dx/(pow(x, p));
return z;
}

int main()
{

ofstream PLIK;

double a, b, s1,s2,s3,s4,x, p; int i;
int n;
s1=0;s3=0;
s2=0;s4=0;

cout.unsetf(ios::floatfield);
cout.precision(16);
PLIK.open("RESULTS.txt");

cout << "ANALYTICALLY." << endl;
PLIK<<"ANALYTICALLY A<<endl;
cout << "SECTION A:" << endl; // Podpunkt pierwszy
for (n = 1; n <= 20; n++)
{

a=1.0; b=2.0;
cout  << n << " ";
p = 1 - pow(10.0, (-n));

s1 = (pow(b, (1 - p)) - (pow(a, (1 - p))))/(1 - p);
cout <<s1<<" " << endl;
PLIK<<s1<<setprecision(16)<<" "<<endl;

}

PLIK<<"ANALYTICALLY B"<<endl;
cout << "ANALYTICALLY " << endl;
cout << "SECTION B:" << endl; // Podpunkt drugii
for (n = 1; n <= 20; n++)
{
a=1.0; p=0.5;
cout << n << " ";
b = 1 + pow(10.0, (-n));

s2 = (pow(b, (1 - p)) - (pow(a, (1 - p))))/(1 - p);
cout << s2<<" " << endl;
PLIK<<s2<<setprecision(16)<<" "<<endl;

}

PLIK<<"SIMPSON A"<<endl;
cout << "SIMPSON RULE" << endl;
cout << "SECTION A" << endl;

for (n = 1; n <= 20; n++)
{
p=1 - (pow(10.0, (-n)));
a=1.0;
cout  << n << " ";
b=2.0;

s3 = (b-a)/ 6 * (f(a) + (4*(f((a+B)/>/2)))+f(B)/>);
cout << s3<<" " << endl;
PLIK<<s3<<setprecision(16)<<" "<<endl;

}

PLIK<<"SIMPSON B"<<endl;
cout << "SIMPSON RULE " << endl;
cout << "SECTION B" << endl;

for (n = 1; n <= 20; n++)
{
a=1.0;p=0.5;
cout << n << " ";
b=1 + pow(10.0, (-n));

s4 = (b-a)/ 6 * (fx(a) + (4*(fx((a+B)/>/2)))+fx(B)/>);
cout <<  s4 << " "  << endl;
PLIK<<s4<<setprecision(16)<<" "<<endl;

}

PLIK.close();

cout<<endl;

```

Is This A Good Question/Topic? 0

## Replies To: Calculate integral using analytically and Simpson methods

### #2 #define

• Duke of Err

Reputation: 1853
• Posts: 6,671
• Joined: 19-February 09

## Re: Calculate integral using analytically and Simpson methods

Posted 06 December 2012 - 08:56 PM

This return is in the for loop, so the loop is only run once.

```016	    return z;}

```

Reputation: 0
• Posts: 4
• Joined: 06-December 12

## Re: Calculate integral using analytically and Simpson methods

Posted 07 December 2012 - 12:32 AM

So I should return nothing? When I doing it my program results are #qnan..

### #4 raghav.naganathan

• Perfectly Squared ;)

Reputation: 410
• Posts: 1,449
• Joined: 14-September 12

## Re: Calculate integral using analytically and Simpson methods

Posted 07 December 2012 - 01:34 AM

Instead of using return in the for loop, you can return it after the for loop closes.Like this.

```013	    for(n=1;n<=20;n++){
014	        p=1 - (pow(10.0, (-n)));
015	        z=1/(pow(x, p));
016	    }
017         return z;
018	}
```

regards,
Raghav

Reputation: 0
• Posts: 4
• Joined: 06-December 12

## Re: Calculate integral using analytically and Simpson methods

Posted 07 December 2012 - 03:23 AM

I was trying write it like this before and It's not working the result for Simposn rule from n=1 to n=20 is the same.

### #6 #define

• Duke of Err

Reputation: 1853
• Posts: 6,671
• Joined: 19-February 09

## Re: Calculate integral using analytically and Simpson methods

Posted 07 December 2012 - 11:39 PM

You can print p and pow(10.0, (-n)) and see that the number loses precision when the power is very small.

```    cout << "ANALYTICALLY." << endl;
PLIK << "ANALYTICALLY A" <<endl;
cout << "SECTION A:" << endl; // Podpunkt pierwszy
for (n = 1; n <= 20; n++)
{

a=1.0; b=2.0, s1=0;
cout  << setw(2)  << n << " ";
p = 1.0 - pow(10.0, (-n));
cout  << setw(20) << scientific << p << " ";
cout  << setw(20) << scientific << pow(10.0, (-n)) << " ";

if(p < 1.0)
s1 = (pow(b, (1 - p)) - (pow(a, (1 - p))))/(1 - p);

cout << s1 << " " <<endl;
// PLIK<<s1<<setprecision(16)<<" "<<endl;

}

cin.get();

```

The data type long double can also be used.