/* ---------------------------------------------------------------------  
// Figure 5.14:  Integration by summing rectangles.
// --------------------------------------------------------------------- 
*/
#include "tools.h"
#define N 100                                                 

/* This is the function that we will integrate. ------------------------ */
double f( double x ){ return x*x + x; }       

void main( void )                                                               
{
    double a = 0.0;         /* Lower limit of integration. */           
    double b = 1.0;         /* Upper limit of integration. */           
    double h = (b - a) / N; /* Width of one of the N rectangles summed.*/

    double x;               /* Current function argument; a <= x < b. */
    double sum;             /* Total area of rectangles. */
    int k;                  /* Loop counter. */                          

    banner();                                                   
    printf( " Integrate x*x + x from %g to %g.\n", a, b );
    
    sum = 0.0;
    k = 0;    
    while (k < N) {         /* Add up N rectangles. */                                                            
        x = a + k * h;      /* Lower left corner of kth rectangle. */                                                   
        sum += h * f( x );  /* Area of rectangle at x. */
        ++k;                                        
    }
    printf( " The area is %g\n", sum );
    bye();
}