Integrate

SciPy

SciPy is a fundamental library for scientific computing (see scipy.org). The documentation of scipy.integrate submodule and the quad function can be found here.

Example: Calculate $\int_0^1 x^2\,\mathrm{d}x$.

from scipy.integrate import quad
quad(lambda x: x**2, 0, 1)[0]

0.33333333333333337

Recall: A lambda function is a small anonymous function, which can only have one expression as a return value.

def sq(x):         # define a named function 
    return x**2
sq(4)              # call the function

16

lambda x: x**2     # define an anonymous function

<function __main__.<lambda>(x)>

_(4)               # call it

16

(lambda x: x**2)(4) # define and call an anonymous function

16

SymPy

SymPy is a Python library for symbolic mathematics. A tutorial for this module and for the integrals can be found here and here.

Example: Calculate $\int x^2\,\mathrm{d}x$ and $\int_0^1 x^2\,\mathrm{d}x$.

from sympy import *
x = Symbol('x')
integrate(x**2, x)

$\displaystyle \frac{x^{3}}{3}$

integrate(x**2, (x, 0, 1))

$\displaystyle \frac{1}{3}$