POJ 2098 数值积分

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#include <cstdio>#include <cstring>#include <cmath>#include <iostream>const double eps = 1E-6;int T;double a, b, l, r;// simpson公式用到的函数double F(double x){return sqrt(b * b * (1 - x * x / (a * a)));}// 三点simpson法。这里要求F是一个全局函数double simpson(double a, double b){double c =  a + (b - a) / 2;return (F(a) + 4 * F(c) + F(b)) * (b - a) / 6;}// 自适应Simpson公式（递归过程）。已知整个区间[a,b]上的三点simpson值Adouble asr(double a , double b , double eps , double A){double c = a + (b - a) / 2;double L = simpson(a, c) , R = simpson(c, b);if (fabs(A - L - R) <= 15 * eps) return L + R + (A - L - R) / 15;return asr(a, c, eps / 2, L) + asr(c, b, eps / 2, R);}// 自适应Simpson公式（主过程）double asr(double a, double b, double eps){return asr(a, b, eps, simpson(a, b));}int main(){scanf("%d", &T);while (T--){scanf("%lf%lf%lf%lf", &a, &b, &l, &r);double ans = asr(l, r, eps);printf("%.3f\n", ans * 2);}return 0;}

求椭圆，套公式即可。

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