HDU 1073 The area

用微积分求面积, 简单的数学题.

求出k, h, a, b, c

y1 = kx + h; y2 = a*x*x + b * x + c;

再求出f (x) = (y1 - y2)的原积函数(x2 ~ x3)

area = F(x3) - F(x2).

2010-11-26　　18:18:36　　Accepted　　10710MS　　216K　　692 B　　C　　Y

 

#include <stdio.h>
#include <stdlib.h>

int main()
{
    int cas;
    double x1, y1, x2, y2, x3, y3, k, h, a, b, c, area;
    
    scanf("%d", &cas);    
    while ( cas-- )
    {
        scanf("%lf%lf", &x1, &y1);
        scanf("%lf%lf", &x2, &y2);
        scanf("%lf%lf", &x3, &y3);
        
        /* y = kx + h */
        k = (y3 - y2) / (x3 - x2);
        h = y2 - k * x2;
        
        /* y = ax*x + b*x + c*/
        a = (((y2 - y1) / (x2 - x1)) - ((y3 - y2) / (x3 - x2))) / (x1 - x3);
        b = ((y2 - y1) / (x2 - x1)) - (a * (x1 + x2));
        c = y3 - (a * x3 * x3 + b * x3);
        
        area = ((a / 3)*x3*x3*x3 + ((b-k)/2)*x3*x3 + (c-h)*x3)
                - ((a / 3)*x2*x2*x2 + ((b-k)/2)*x2*x2 + (c-h)*x2);
        
        printf("%.2lf\n", area);
    }

    return 0;
}

 

Problem DescriptionIgnatius bought a land last week, but he didn't know the area of the land because 

the land is enclosed by a parabola and a straight line. The picture below shows the area. Now given all 

the intersectant points shows in the picture, can you tell Ignatius the area of the land?Note: 

The point P1 in the picture is the vertex of the parabola.

 

Input

The input contains several test cases. The first line of the input is a single integer T which is the number 

of test cases. T test cases follow.Each test case contains three intersectant points which shows in the picture, 

they are given in the order of P1, P2, P3. 

Each point is described by two floating-point numbers X and Y(0.0<=X,Y<=1000.0).

Output

For each test case, you should output the area of the land, the result should be rounded to 2 decimal places.

Sample Input

2

5.000000 5.000000

0.000000 0.000000

10.000000 0.000000

10.000000 10.000000

1.000000 1.000000

14.000000 8.222222

Sample Output

33.33

40.69