//-------------------------------------------------------------------
//	traprule.cpp
//
//	This program uses the Trapezoid Rule to compute a value for
//	the definite integral of a function f(x) from x=a to x=b.
//
//		compile using:  $ make traprule
//		execute using:  $ traprule
//
//	programmer: ALLAN CRUSE
//	written on: 19 SEP 2005
//-------------------------------------------------------------------

#include <stdio.h>	// for printf(), perror() 
#include <math.h>	// for exp(), log(), sin(), cos(), etc

double func( double x )
{
	double	y = x*x;
	return	y;
}

int main( int argc, char **argv )
{
	double	a = 0.0, b = 1.0;
	int	n = 10;
	double	deltaX = (b - a)/n;

	printf( "\n\tNUMERICAL INTEGRATION USING TRAPEZOID RULE \n" );
	printf( "\nIntegral is from  a = %1.2f  to  b = %1.2f ", a, b );  
	printf( " with  n = %d  subintervals \n", n );

	// show the function's value at each point-of-subdivision
	for (int i = 0; i <= n; i++)
		{
		double	xi = a + i * deltaX;
		double	yi = func( xi );
		printf( "\n\tx%d\t%1.2f\t%1.6f", i, xi, yi ); 
		}
	printf( "\n" );

	// compute the integral's approximating sum by Trapezoid Rule
	double	summation = 0.0;
	for (int i = 1; i < n; i+=2)
		{
		double	xi = a + i * deltaX;
		double	y0 = func( xi - deltaX );
		double	y1 = func( xi );
		double	y2 = func( xi + deltaX );
		summation += (y0 + 2*y1 + y2); 
		}
	double	integral = (deltaX / 2)*summation;
	
	// display the result of the foregoing computation
	printf( "\nThe integral is approximately %1.6f \n\n", integral );
}