Simpson's rule 3/8 for n intervals in Python

im trying to write a program that gives the integral approximation of e(x^2) between 0 and 1 based on this integral formula: Formula

i've done this code so far but it keeps giving the wrong answer (Other methods gives 1.46 as an answer, this one gives 1.006).

I think that maybe there is a problem with the two for cycles that does the Riemman sum, or that there is a problem in the way i've wrote the formula. I also tried to re-write the formula in other ways but i had no success

Any kind of help is appreciated.

import math  import numpy as np    def f(x):      y = np.exp(x**2)      return y    a = float(input("¿Cual es el limite inferior? \n"))  b = float(input("¿Cual es el limite superior? \n"))  n = int(input("¿Cual es el numero de intervalos? "))    x = np.zeros([n+1])  y = np.zeros([n])  z = np.zeros([n])    h = (b-a)/n    print (h)    x[0] = a  x[n] = b      suma1 = 0  suma2 = 0    for i in np.arange(1,n):      x[i] = x[i-1] + h      suma1 = suma1 + f(x[i])    alfa = (x[i]-x[i-1])/3    for i in np.arange(0,n):      y[i] = (x[i-1]+ alfa)      suma2 = suma2 + f(y[i])      z[i] = y[i] + alfa      int3 = ((b-a)/(8*n)) * (f(x[0])+f(x[n]) + (3*(suma2+f(z[i]))) + (2*(suma1)))    print (int3)  

https://stackoverflow.com/questions/66739301/simpsons-rule-3-8-for-n-intervals-in-python March 22, 2021 at 09:34AM