HDU1724[辛普森公式求积分]Ellipse

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 
    
     

题意：要你求l与r之间椭圆的面积
分析：用辛普森公式求积分


简单模板题直接套

#include<stdio.h>
#include<math.h>
#define eps 1e-9
double a,b,l,r;
double F(double x)
{
    return 2*b*sqrt(1.0-x*x/(a*a));
}
double cal(double l,double r)
{
    return (r-l)/6.0*(F(r)+4.0*F((r+l)/2.0)+F(l));
}
double simpson(double l,double r)
{
    double m=(l+r)/2.0;
    double fl=cal(l,m),fr=cal(m,r);
    if(fabs(fl+fr-cal(l,r))<eps) return fr+fl;
    else return simpson(l,m)+simpson(m,r);
}
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%lf%lf%lf%lf",&a,&b,&l,&r);
        printf("%.3lf\n",simpson(l,r));
    }
    return 0;
}