HDU 1071 The area （数学求定积分）

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

纯粹的数学积分题。

#include <iostream>
#include <cstdio>
#include <cmath>
using namespace std;
/*设抛物线方程为 y = a(x - b)^2 + c; 直线方程为 y = kx + d;*/
double a, b, c, d, k;
double fun(double x){
    return a*x*x*x/3 - (2*a*b+k)*x*x/2 + (a*b*b+c-d)*x; 
}

int main() {
    int t;
    scanf("%d", &t);
    while(t--) {
        double x1, y1, x2, y2, x3, y3;
        scanf("%lf%lf%lf%lf%lf%lf", &x1, &y1, &x2, &y2, &x3, &y3);
        b = x1;
        c = y1;
        a = (y2 - y1)/(x2 - x1)/(x2 - x1);
        k = (y3 - y2)/(x3 - x2); 
        d = y2 - k*x2;
        printf("%.2f\n", fabs(fun(x2) - fun(x3)));
    }
    return 0;
}