# Numerical Integration Using Simpson 1/3 Method C Program

C Program for approximating definite integral of a continuous function using Simpson's 1/3 Rule (Method)

## Simpson 1/3 Rule C Program

``````
#include<stdio.h>
#include<conio.h>
#include<math.h>

/* Define function here */
#define f(x) 1/(1+x*x)

int main()
{
float lower, upper, integration=0.0, stepSize, k;
int i, subInterval;
clrscr();
/* Input */
printf("Enter lower limit of integration: ");
scanf("%f", &lower);
printf("Enter upper limit of integration: ");
scanf("%f", &upper);
printf("Enter number of sub intervals: ");
scanf("%d", &subInterval);

/* Calculation */
/* Finding step size */
stepSize = (upper - lower)/subInterval;

/* Finding Integration Value */
integration = f(lower) + f(upper);
for(i=1; i<= subInterval-1; i++)
{
k = lower + i*stepSize;
if(i%2==0)
{
integration = integration + 2 * f(k);
}
else
{
integration = integration + 4 * f(k);
}
}
integration = integration * stepSize/3;
printf("\nRequired value of integration is: %.3f", integration);
getch();
return 0;
}
``````

## Simpson's 1/3 Rule C Program Output

```Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6

Required value of integration is: 0.785
```