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

#### Algorithm:

```Step 1.  Read x1, x2, e {x1 and x2 are the two end points of the internal the allowed error in integral is e}
Step 2.  h = x2 - x1
Step 3.  SI = (f(x1) + f(x2))/2;
Step 4.  I = h - si
Step 5.  i = 1 Repeat
Step 6.  x = x1 + h/2
Step 7.  for J= 1 to I do
Step 8.  SI = SI + f(x)
Step 9.  x = x + h
End for

Step 10. i = 21
Step 11. h = h/2 {Note that the internal has been halved above and the number of points where the function has to be computed is doubled}
Step 12. i0 = i1
Step 13. i1 = h.si
Step 14. until / I1 - i0 / <= c./i1/
Step 15. Write I1, h, i
Step 16. Stop.```

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

```#include<stdio.h>
#include<math.h>
main()
{
float h, a, b, n, x, y, sum = 0, integral;
int i;
clrscr();
printf("enter the value of a, b, n:");
scanf("%f %f %f", &a, &b, &n);
printf("enter the values of x:");
for(i = 0; i <= (n-1); i++)
{
scanf("%f", &x[i]);
}
printf("\n enter the values of y:");
for(i = 0; i <= (n-1); i++)
{
scanf("%f", &y[i]);
}
h = (b-a)/n;
x = a;
for(i = 1; i <= n-1; i++)
{
x[i] = x[i-1] + h;
sum = sum + 2 * y[i];
}
sum = sum + y[b];
integral = sum * (h/2);
printf("approximate integral value is: %f", integral);
getch();
}```

#### Input & Output:

```enter the values of a, b, n
123
enter the values of x:
123
enter the values of y:
123
approximate integral value is 2.166667```
• Updated
Oct 21, 2014
• Views
21,284
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