# Write a C program to implement `Simpson method`.

#### Algorithm:

```Step 1.  Read x1, x2, e
Step 2.  h = (x2 - x1)/2
Step 3.  i = 2
Step 4.  si = f(x1) + f(x2)
Step 5.  s2 = 0
Step 6.  s4 = f(x1 + h)
Step 7.  I0 = 0
Step 8.  In = (s + 4s4).(h/3)

Repeat

Step 9.  s2 = s2 + s4 { s2 stores already computed functional value and s4 the value computed in the new nitration }
Step 10. s4 = 0
Step 11. x = x1 + h/2
Step 12. for j = 1 to I do
Step 13. s4 = s4 + f(x)
Step 14. x = x + h
Step 15. h = h/2
Step 16. i = 2i
Step 17. io = in
Step 18. in = (s1 + 2s2 + 4s4) . (h/3)
Step 19. until |In-Io|≤e. /in
Step 20. Write In, h, i
Step 21. STOP```

#### Flowchart: #### Program:

```#include<stdio.h>
#include<conio.h>
#include<math.h>
main()
{
float h, a, b, n, x, y, sum = 0, itgl;
int i;
clrscr();
printf("enter the values of a, b, n");
scanf("%f%f%f", &a, &b, &n);
printf("enter the values of x");
for(i = 0; i <= n; i++)
{
scanf("%f", &x[i]);
}
printf("\n enter the values of y");
for(i = 0; i <= n; i++)
{
scanf("%f", &y[i]);
}
h = (b - a)/n;
a = x;
b = x[n];
for(i = 0; i <= (n-2); i++)
{
x[i] = x[i] + h;
if(i % 2 == 0)
{
sum = sum + 4 * y[i];
}
else
{
sum = sum + 2 * y[i];
}
}
itgl = sum * (h/3);
printf("integral value%f", itgl);
getch();
}```

#### Input & Output:

```enter the values of a, b, n
123
enter the value of x
4567
enter the values of y
8912
integral value is 5.555556```
• Updated
Nov 05, 2014
• Views
6,844
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