C program to implement Trapezoidal method

       Ex:

       Formula:

               Here x₀=0 and x₀+nh=6  hence h= (6-0)/4 =1.5

 therefor interval is 1.5 in each term 

               lower bound                                                upper bound

x	0	1.5	3	4.5	6
f(x)	1	.30	.10	.04	.02

Now apply the trapezoidal formula :

 = 1.5/2[(1+.02) +2(.30+.10+.04)]

   = 1.5/2[1.027+2(.44)]

   =1.5/2[1.027+.88)]

   =1.5/2[1.907]   =1.4

C Code:

#include<stdio.h>

float f(float);

void main()

{ float a,b,h,i,n,k=0;

   printf("\nEnter the lower and upper limits for function");

   scanf("%f%f",&a,&b);

   printf("\nEnter the difference");

   scanf("%f",&h);

//Calculate the integral

printf("\nx\tf(x)");

for(i=a;i<=b;i=i+h)

{ printf("\n%f\t%f",i,f(i));

k=k+f(i);

}

k=k-(f(a)+f(b));

k=(h/2.0)*(f(a)+f(b))+h*k;

printf("\nThe definite integral=%f",k);

}

float f(float x)

{ return(1/(1+x*x));

}

Output:

Enter the lower and upper limits for function

0                                                                 

6                                                                                                                  

Enter the difference 1.5                                                                                                                        

x                f(x)                                                                                                             

0.000000        1.000000                                                                                                         

1.500000        0.307692                                                                                                         

3.000000        0.100000                                                                                                         

4.500000        0.047059                                                                                                         

6.000000        0.027027                                                                                                         

The definite integral= 1.452397