本文通过Python的Scipy库实现对半球体体积的数值积分计算，并对比了理论值π/6。代码中定义了半圆和半球面方程，利用dblquad函数进行双积分计算。
from scipy import integrate
import numpy as np
import time
start=time.clock()
def half_circle(x):
return (1-x**2)**0.5
def half_sphere(x,y):
return (1-x**2-y**2)**0.5
volume,error=integrate.dblquad(half_sphere,-1,1,
lambda x: -half_circle(x),
lambda x: half_circle(x))
end=time.clock()
print('{}\n{}\n{}'.format(volume,error,np.pi*4/3/2))
print('time={} Sconds'.format(end-start))
import numpy as np
import time
start=time.clock()
def half_circle(x):
return (1-x**2)**0.5
def half_sphere(x,y):
return (1-x**2-y**2)**0.5
volume,error=integrate.dblquad(half_sphere,-1,1,
lambda x: -half_circle(x),
lambda x: half_circle(x))
end=time.clock()
print('{}\n{}\n{}'.format(volume,error,np.pi*4/3/2))
print('time={} Sconds'.format(end-start))
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