HDU1724 - 积分

Ellipse

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 876    Accepted Submission(s): 280


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

 

Author

威士忌

 

Source

HZIEE 2007 Programming Contest

简单高数题.

#include<iostream>
#include<cstdio>
#include<cmath>
using namespace std;
double a,b,l,r;
double f(double x)
{
double t=asin(x/a);
return 0.5*a*b*(t+0.5*sin(2*t));
}
int main()
{
int T;
cin>>T;
while(T--)
{
cin>>a>>b>>l>>r;
printf("%.3lf\n",2*(f(r)-f(l)));
}
return 0;
}