补一下一些小盲区，譬如simpson这种数值积分的方法虽然一直知道，但是从未实现过，做一道例题存一个模板。
#pragma warning(disable:4996)
#include<iostream>
#include<cstring>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
using namespace std; double a, b, l, r; double sqr(double x){
return x*x;
} double f(double x){
return b / a*sqrt(sqr(a) - sqr(x));
} double simpson(double l, double r)
{
return (f(l) + 4 * f((l + r) / 2) + f(r))*(r - l) / 6;
} double simpson(double l, double r, double all, double eps){
double m = (l + r) / 2;
double L = simpson(l, m), R = simpson(m, r);
if (fabs(L + R - all) <= 15 * eps) return L + R + (L + R - all) / 15;
return simpson(l, m, L, eps / 2.0) + simpson(m, r, R, eps / 2.0);
} double simpson(double l, double r, double eps){
return simpson(l, r, simpson(l, r), eps);
} int main()
{
int T; cin >> T;
while (T--){
cin >> a >> b >> l >> r;
printf("%.3lf\n", 2*simpson(l, r, 1e-4));
}
return 0;
}