# How to Use the Scipy integrate.quad() Method in Python

09/17/2021

Contents

The scipy.integrate.quad() method is a function from the scipy.integrate module that computes a definite integral of a given function over a specified interval. The integral is calculated using the Gauss-Kronrod quadrature algorithm, which is a widely used numerical integration method.

Here’s how to use scipy.integrate.quad() method in Python:

##### Import the necessary modules:
``import scipy.integrate as integrate``
##### Define the function you want to integrate:

The function should take a single argument (the variable of integration) and return a single value:

``````def integrand(x):
return x**2
``````

Call the quad() method with the integrand function and the limits of integration as arguments. The limits of integration should be specified as a tuple (lower limit, upper limit):

``result, error = integrate.quad(integrand, 0, 1)``
##### The quad() method returns two values:

The result of the integration and an estimate of the error in the result. You can assign these values to variables for later use:

``print(result, error)``

Putting it all together, here’s an example that integrates the function x^2 over the interval [0, 1]:

``````import scipy.integrate as integrate

def integrand(x):
return x**2

result, error = integrate.quad(integrand, 0, 1)

print(result, error)
``````

The output should be 0.33333333333333337 3.700743415417189e-15, which is the result of the integration and an estimate of the error.