# coding: utf-8

# # Computing the weights in Simpson's rule

# In[3]:

import numpy as np
import numpy.linalg as la


# We found the integrals:
# 
# $$
# \begin{align*}
# \int_0^1 1 dx &= 1\\
# \int_0^1 x dx &= \frac 12 \\
# \int_0^1 x^2 dx &= \frac 13 \\
# \end{align*}
# $$
# 

# In[4]:

integrals = np.array([1, 1/2, 1/3])


# In[6]:

nodes = np.linspace(0, 1, 3)
nodes


# In[8]:

V = np.array([
1+0*nodes,
nodes,
nodes**2
]).T
V


# Now compute the weights:

# In[11]:

la.inv(V).T.dot(integrals)


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