import numpy as np
from scipy import integrate
 
 
def half_circle(x):
  """
  原心：(1,0),半径为1
  半圆函数：(x-1)^2+y^2 = 1
  """
  return (1-(x-1)**2)**0.5
 
"""
梯形法求积分：半圆线和x轴包围的面积
"""
N = 10000
x = np.linspace(0,2,num=N)#,endpoint=True)
dh = (2-0)/N
y = half_circle(x)
"""
梯形法求积分：（上底+ 下底）*高/2
"""
S = sum((y[1:]+y[:-1])*dh/2)
 
print("=========%s=========="%"梯形法")
print("面积：%f"%S)
 
"""
直接调用intergrate的积分函数quad
"""
S2,err = integrate.quad(half_circle,0,2)
 
print("=========%s=========="%"quad")
print("面积：%f"%S2)
 
 
"""
多重定积分:注意积分顺序
"""
def half_sphere(y,x):
  """
  球心：（1，0，0）
  半径：1
  半球：(x-1)^2+y^2+z^2=1
  """
  return (1-(x-1)**2-y**2)**0.5
 
"""
积分顺序：
v = V x in [0,2] :V y in [-g(x),h(x)]
"""
V3,err = integrate.dblquad(half_sphere,0,2,lambda x:-half_circle(x),lambda x:half_circle(x))
print("========%s==========="%"dblquad")
print("体积：%f"%V3)