//-------------------------------------------------------------------
//	areademo.cpp
//
//	This program illustrates successive approximations to the
//	area under the graph  y = x*x  from  x=0  to  x=1  using
//	sums of areas of inscribed and circumscribed rectangles.
//
//	      compile using:  $ g++ areademo.cpp -o areademo
//	      execute using:  $ ./areademo
//
//	programmer: ALLAN CRUSE
//	written on: 19 APR 2006
//-------------------------------------------------------------------

#include <stdio.h>	// for printf(), perror() 

#define	N_MAX	100000

int main( int argc, char **argv )
{
	printf( "\n  Area under the graph  y = x*x  from  x=0  to  x=1 \n\n" );

	for (int n = 1; n < N_MAX; n+=n)
		{
		float	deltaX = 1.0/n;
		float	area_A = 0.0;
		float	area_B = 0.0;
		for (int k = 1; k <= n; k++)
			{
			float	x_L = ((float)(k-1))/n;
			float	x_R = ((float)(k))/n;
			float	y_B = x_L * x_L;
			float	y_A = x_R * x_R;
			area_A += y_A * deltaX;
			area_B += y_B * deltaX;
			}
		printf( "     n = %-8d   ", n );
		printf( "%1.5f  <  AREA  <  %1.5f \n", area_B, area_A );
		}

	printf( "\n" );
}