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。

#include <bits/stdc++.h>
using namespace std;
int T;
double z1, z2, V, area;
const double pai = acos(-1.0);
double getV()
{
    double x1 = 4.5*z1 + 4*sin(z1) + 0.25*sin(2*z1);
    double x2 = 4.5*z2 + 4*sin(z2) + 0.25*sin(2*z2);
    return pai*(x2-x1);
}
double fun(double x)
{
    return 2*pai*(2+cos(x))*sqrt(1.0+sin(x)*sin(x));
}
double getpart(double x, double y)
{
    double ans = 0;
    double cut = (y-x)/5000;
    double low = x, high;
    for(int i = 1; i <= 5000; i++)
    {
        high = low+cut;
        ans += (fun(low) + fun(high))/2*cut;
        low += cut;
    }
    return ans;
}
int main()
{
    scanf("%d", &T);
    while(T--)
    {
        scanf("%lf%lf", &z1, &z2);
        if(z1 > z2) swap(z1, z2);

        V = getV();
        int cnt = int((z2-z1)/(pai*2));
        area = pai*(2+cos(z1))*(2+cos(z1));
        area += getpart(z1, z1+2*pai)*cnt;
        area += getpart(z1+2*pai*cnt, z2);
        printf("%.8lf %.8lf
", V, area);

    }
    return 0;
}