python 求简单定积分

在某个微信群里看到个积分题目，说是用六年级的知识解？？？其实根据后面运行的结果来看，手算可能不太行。

import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
import numpy as np

x1 = np.arange(-4,4,0.01)
y1 = (16-x1**2)**0.5
x2 = np.arange(-2,6,0.01)
y2 = (16-(x2-2)**2)**0.5

plt.figure(figsize=(15,7))
plt.plot(x1,y1)
plt.plot(x2,y2)
plt.grid()
plt.show()

计算交点横坐标

import sympy
x = sympy.symbols("x")
a = sympy.solve([(16-x**2)**0.5-(16-(x-2)**2)**0.5],[x])
print(a)

[(1.00000000000000,)]

计算交点纵坐标

y = (16-(1-2)**2)**0.5
y

3.872983346207417

from scipy.integrate import tplquad,dblquad,quad 
#积分
val1,err1=quad(lambda x:(16-(x-2)**2)**0.5,#函数
               -2,#x下界
               1)#x上界
print ("积分结果:",val1)

积分结果: 8.608436900118841

print ("阴影部分面积:",0.5*np.pi*(4**2)-val1*2)

阴影部分面积: 7.915867428480663