Write a program to find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. The area under a curve between two points can be found by doing a definite integral between the two points.

#include 
float
    start_point,            /* GLOBAL VARIABLES */



    end_point,
    total_area;
int
    numtraps;
main( )
{
   void
    input(void
);
   float
    find_area(float
 a,float
 b,int
 n); /* prototype */




   print(“AREA UNDER A CURVE”);
   input( );
   total_area = find_area(start_point, end_point, numtraps);
   printf(“TOTAL AREA = %f”, total_area);
}
void
 input(void
)
{
   printf(“\n Enter lower limit:”);
   scanf(“%f”, &start_point);
   printf(“Enter upper limit:”);
   scanf(“%f”, &end_point);
   printf(“Enter number of trapezoids:”);
   scanf(“%d”, &numtraps);
}
float
 find_area(float
 a, float
 b, int
 n)
{
      float
base
, lower, h1, h2;    /* LOCAL VARIABLES */


float
 function_x(float
 x);    /* prototype */


float
 trap_area(float
 h1,float
 h2,float
base
);/*prototype*/


base
 = (b-1)/n;
         lower = a;
       for
(lower =a; lower <= b-base
; lower = lower + base
)
    {
    h1  =  function_x(lower);
             h1  =  function_x(lower + base
);
             total_area += trap_area(h1, h2, base
);
    }
return
(total_area);
    float
 trap_area(float
 height_1,float
 height_2,float
base
)
        {
       float
 area;    /* LOCAL VARIABLE */



       area = 0.5 * (height_1 + height_2) * base
;
         return
(area);
    }
    float
 function_x(float
 x)
    {
         /* F(X) = X * X + 1 */


return
(x*x + 1);
    }
    
Output

    AREA UNDER A CURVE
    Enter lower limit: 0
    Enter upper limit:  3
    Enter number of trapezoids: 30
    TOTAL AREA   =  12.005000

    AREA UNDER A CURVE
    Enter lower limit: 0
    Enter upper limit: 3
    Enter number of trapezoids: 100
    TOTAL AREA = 12.000438