hdu 1724 Ellipse (辛普森积分)

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=PI*a*b )

 

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

 

求一个椭圆[l,r]之间的面积

#include <bits/stdc++.h>

using namespace std;
int t;
const double esp = 1e-10;
double a,b;
double f (double x)
{
    return b*sqrt(1.0-(x*x)/(a*a));
}
double simpson (double l,double r)
{
    return (f(l)+4*f((l+r)/2.0)+f(r))/6.0*(r-l);
}
double integral (double l,double r)
{
    double mid = (l+r)/2.0;
    double res = simpson(l,r);
    if (fabs(res-simpson(l,mid)-simpson(mid,r)) < esp)
        return res;
    else
        return integral(l,mid) + integral(mid,r);
}
int main()
{
    //freopen("de.txt","r",stdin);
    scanf("%d",&t);
    while (t--){
        double l,r;
        cin>>a>>b>>l>>r;
        printf("%.3lf
",integral(l,r)*2);
    }
    return 0;
}