# Integration of functions when you have a formula
# for the function

def fun1(x):
    return x**3

def fun2(x,p):
    return np.sin(p*x)

import numpy as np
from scipy import integrate

# Integrate fun1 from 0 to 1 using the quad
# function.  This uses a more sophisticated process
# than MATLAB's integral function.

# The result is returned as a tuple.
#   s[0] = approximate value of integral
#   s[1] = upper bound on error of approximation
s1 = integrate.quad(fun1,0,1)
print('s1 = ',s1)

# You can also handle integrals that have parameters
#     lambda x:  in Python
# has the same effect as
#     @(x)       in MATLAB
p = 4
s2 = integrate.quad(lambda x: fun2(x,p),0,1)
print('s2 = ',s2)