ZOJ 3898 Stean 矩形法求积分

题目链接：http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemId=5601

题意：求一个绕y轴旋转的旋转体体积。R = 2+cos(z)。

思路：旋转体体积可以直接用积分求出来，旋转体表面积公式对于此题积分比较难积，所以用矩形法来求积分。

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 int T;
 4 double z1, z2, V, area;
 5 const double pai = acos(-1.0);
 6 double getV()
 7 {
 8     double x1 = 4.5*z1 + 4*sin(z1) + 0.25*sin(2*z1);
 9     double x2 = 4.5*z2 + 4*sin(z2) + 0.25*sin(2*z2);
10     return pai*(x2-x1);
11 }
12 double fun(double x)
13 {
14     return 2*pai*(2+cos(x))*sqrt(1.0+sin(x)*sin(x));
15 }
16 double getpart(double x, double y)
17 {
18     double ans = 0;
19     double cut = (y-x)/5000;
20     double low = x, high;
21     for(int i = 1; i <= 5000; i++)
22     {
23         high = low+cut;
24         ans += (fun(low) + fun(high))/2*cut;
25         low += cut;
26     }
27     return ans;
28 }
29 int main()
30 {
31     scanf("%d", &T);
32     while(T--)
33     {
34         scanf("%lf%lf", &z1, &z2);
35         if(z1 > z2) swap(z1, z2);
36 
37         V = getV();
38         int cnt = int((z2-z1)/(pai*2));
39         area = pai*(2+cos(z1))*(2+cos(z1));
40         area += getpart(z1, z1+2*pai)*cnt;
41         area += getpart(z1+2*pai*cnt, z2);
42         printf("%.8lf %.8lf
", V, area);
43 
44     }
45     return 0;
46 }