用python实现牛顿-柯特斯公式

import numpy as np
import math
from scipy import integrate

def f(x):
    return math.exp(-x**2)

def g(x):
    return math.exp(-x**2)

def func(a,b,n,g):

    x = np.linspace(a,b,n+1)

    sum1 = 0
    
    h =(b-a)/n

    for i in range(n):
        
        if i%2 == 0:
            
            sum1 = sum1 + 2*g(x[i])
        
        if i%2 != 0:
            
            sum1 = sum1 + 4*g(x[i])
            
    sum1 = (h/3)*(sum1 -g(x[0])-g(x[n]))
            
    return sum1

answer = func(0,1,1000,g)
print(answer)

value, error = integrate.quad(f,0, 1)
print(value,error)

结果
0.7467996075163496
0.7468241328124271 8.291413475940725e-15