HDU1724 Ellipse

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=PI*a*b ) 

InputInput 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).OutputFor 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

几何

simpson积分强行搞

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
using namespace std;
const double eps=1e-9;
const int mxn=100010;
int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0' || ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0' && ch<='9'){x=x*10-'0'+ch;ch=getchar();}
    return x*f;
}
int a,b;
inline double f(double x){
    return b*sqrt((double)1-(x*x/(double)a/a));
}
inline double sim(double l,double r){
    return (r-l)/6*(f(l)+4*f((l+r)/2)+f(r));
}
double solve(double l,double r){
    double mid=(l+r)/2;
    double res=sim(l,r);
//    printf("l:%.3f  r:%.3f  res:%.3f
",l,r,res);
    if(fabs(sim(l,mid)+sim(mid,r)-res)<=eps)return res;
    return solve(l,mid)+solve(mid,r);
}
int main(){
    int T=read();
    double l,r;
    while(T--){
        a=read();b=read();
        l=read();r=read();
        double ans=solve(l,r);
        printf("%.3f
",2*ans);
    }
    return 0;
}