HDU-1724 Simpson公式

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Problem Description
Math is important!! Many students failed in 2+2’s mathematical test, so let’s AC this problem to mourn for our lost youth…
Look this sample picture:

A ellipses in the plane and center in point O. the L,R lines will be vertical through the X-axis. The problem is calculating the blue intersection area. But calculating the intersection area is dull, so I have turn to you, a talent of programmer. Your task is tell me the result of calculations.(defined PI=3.14159265 , The area of an ellipse A=PIab )
Input
Input may contain multiple test cases. The first line is a positive integer N, denoting the number of test cases below. One case One line. The line will consist of a pair of integers a and b, denoting the ellipse equation , A pair of integers l and r, mean the L is (l, 0) and R is (r, 0).
(-a <= l <= r <= a).
Output
For each case, output one line containing a float, the area of the intersection, accurate to three decimals after the decimal point.
Sample Input
2
2 1 -2 2
2 1 0 2
Sample Output
6.283
3.142
模板：

#include<bits/stdc++.h>
using namespace std;
inline int read(){
    int x=0,f=0;char ch=getchar();
    while(ch>'9'||ch<'0')f|=ch=='-',ch=getchar();
    while(ch>='0'&&ch<='9')x=(x<<3)+(x<<1)+(ch^48),ch=getchar();
    return f?-x:x;
}
int a,b,l,r;
double F(double x){//目标积分函数
	return sqrt(a*a-x*x);
}
double simpson(double a,double b){
	double c=a+(b-a)/2;
	return (F(a)+4*F(c)+F(b))*(b-a)/6;
}
double 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(L+R-A)<=15*eps) return L+R+(L+R-A)/15.0;
	return asr(a,c,eps/2,L)+asr(c,b,eps/2,R);
}
//调用这个 a左 b右
double asr(double a,double b,double eps){
	return asr(a,b,eps,simpson(a,b));
}
int main(){
 	int t=read();
 	while(t--){
		a=read(),b=read(),l=read(),r=read();
		printf("%.3lf\n",2.0*b*asr(l,r,1e-6)/a);
 	}
	return 0;
}