The area （hdu1071）积分求面积

The area

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 7066 Accepted Submission(s): 4959

Problem Description

Ignatius 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

Hint

For float may be not accurate enough, please use double instead of float.

 

 

 

一道高数题。

 

回顾一下微积分的知道，曲面的微积分。两个方程相减，对x或者y积分，就是面积。

然后具体的公式详见代码把，

ps：http://acm.hdu.edu.cn/showproblem.php?pid=1071

 

 

#include<stdio.h>

//#include<math.h>与y1方法重载了、

double x1,y1,x2,y2,x3,y3;

double area;

double l,h,a,k,b;



//曲线的方程可用顶点式  y = a(x-h)^2+l, (h,l) 为顶点坐标）

//直线方程  y = kx+b；



//图形一定，只是点的位置不定。所以对x积分

double f(double x)

{

    return (a*x*x*x/3)-(a*h+k/2)*x*x+(a*h*h+l-b)*x;//积分,化简

}

int main()

{



    int T;

    scanf("%d",&T);

    while(T--)

    {

        scanf("%lf%lf%lf%lf%lf%lf",&x1,&y1,&x2,&y2,&x3,&y3);

        h=x1;

        l=y1;

        a=(y2-y1)/((x2-h)*(x2-h));

        k=(y3-y2)/(x3-x2);

        b=y2-k*x2;

        printf("%.2lf\n",f(x3)-f(x2));

    }

    return 0;

}