1 #include <bits/stdc++.h> 2 using namespace std; 3 const double eps = 1e-5; 4 double a, b, l, r; 5 6 double F(double x) { 7 //Simpson公式用到的函数 8 return sqrt((a * a * b * b - b * b * x * x) / a / a); 9 } 10 double simpson(double a, double b) { //三点Simpson法，这里要求F是一个全局函数 11 double c = a + (b - a) / 2; 12 return (F(a) + 4 * F(c) + F(b))*(b - a) / 6; 13 } 14 double asr(double a, double b, double eps, double A) { //自适应Simpson公式（递归过程）。已知整个区间[a,b]上的三点Simpson值A 15 double c = a + (b - a) / 2; 16 double L = simpson(a, c), R = simpson(c, b); 17 if (fabs(L + R - A) <= 15 * eps)return L + R + (L + R - A) / 15.0; 18 return asr(a, c, eps / 2, L) + asr(c, b, eps / 2, R); 19 } 20 double asr(double a, double b, double eps) { 21 return asr(a, b, eps, simpson(a, b)); 22 } 23 24 25 int main(){ 26 int n; 27 //freopen("in.txt", "r", stdin); 28 scanf("%d", &n); 29 for(int i = 0; i < n; i++){ 30 scanf("%lf %lf %lf %lf", &a, &b, &l, &r); 31 printf("%.3lf ", 2 *asr(l, r, eps)); 32 } 33 }