Thread: area estimation of graph

hihi,everyone.
As I'm just a beginner of C program, please help ^^.
I use the following program to estimate the area of
y=sqr(cos(x)p2+1)

sqr= square root,
p2 = power 2,

from x=0 to x=2.
I use a rectangle to enclose the graph with height 1.5 and width 2.0.
y<= 2 power 0.5 = 1.414 as cos(x)<=1

so i use this estimation formula:
red_area=rect*(red/total)

if y<1.414, then the pts lie in the graph.
if y>1.414, then the pts lie outside the graph.
for x between 0 and 2.0 with increment 0.00001.

and my program is the following.


# include <stdio.h>
# include <math.h>

int main(void)
{
float y,rect;
float x=0;
int total,red=0;
y=pow(pow(cos(x),2)+1, 0.5);
rect=1.5*2.0;
for (x=0; x<2; x=x+0.00001)
{
total++;
if (y<1.414)
{
red++;
}
}
printf("red area = %f \n", rect*red/total);
return 0;
}


please help me, thanks.

estimating the area of graph by many small rectangles will be a better way.

You can use the following code to do a numerical estimate of the definate integral (which is really what you want):

Code:

double y(double x);
double integrate(double lowerBound, double upperBound, int numRects);

double y(double x){
	return sqrt(pow(cos(x),2) + 1.0);
}

double integrate(double lowerBound, double upperBound, int numRects){
	//computes area by left hand rectangle approximation.
	double rectWidth;
	double area;
	int i;
	area = 0;
	rectWidth = (upperBound - lowerBound)/(double)numrects;
	for (i = 0; i < numRects; i++){
		area += y(lowerBound + rectWidth * (double) i) *rectWidth;
	}
	return area;
}

As numrects increases, this will better and better approximate the integral. In fact, for any integrable funtion, by definition this converges to the integral as numRects goes to infinity.

Ok,it's fine.

thank you very much.^^