The area

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.

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

33.33
40.69

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

题意：给定一个抛物线的顶点P1坐标和另外两点坐标P2、P3，以及一条穿过P2、P3的直线。求直线与抛物线围城的面积。

题解：每次做磊哥出的题总会学到些新东西。这次也不例外。这是我第一次做积分的题。高数总算是没白学。可是已知抛物线三点坐标求抛物线的方程我愣是没解出来，感觉太复杂了，在网上找的别人推出好的公式：click here

#include <stdio.h>

int main()
{
    int t;
    double x1, y1, x2, y2, x3, y3, a, b, c, k, d, p, q, r, ans;
    scanf("%d", &t);
    while(t--){
        scanf("%lf%lf%lf%lf%lf%lf", &x1, &y1, &x2, &y2, &x3, &y3);
        p = y1 / ((x1 - x2) * (x1 - x3));
        q = y2 / ((x2 - x1) * (x2 - x3));
        r = y3 / ((x3 - x1) * (x3 - x2));
        a = p + q + r;
        b = -p*(x2 + x3) - q*(x1 + x3) - r * (x1 + x2);
        c = p * x2 * x3 + q * x1 * x3 + r * x1 * x2;
        k = (y3 - y2) / (x3 - x2);
        d = y2 - k * x2;
        ans = (1.0/3*a*x3*x3*x3 + 1.0/2*(b-k)*x3*x3 + (c-d)*x3) - 
            (1.0/3*a*x2*x2*x2 + 1.0/2*(b-k)*x2*x2 + (c-d)*x2);
        if(ans < 0) ans = -ans;
        printf("%.2lf\n", ans);
    }
    return 0;
}