What is the scipy.integrate.fixed_quad method?

Overview

SciPy is a package in Python that provides functions that can be used for numerical and mathematical computation. The integrate sub-package in SciPy implements general-purpose integration methods in Python. The scipy.integrate.fixed_quad method in SciPy computes a definite integral using a simple Gaussian quadrature of the fixed order n.

Syntax

scipy.integrate.fixed_quad(func, a, b, args=(), n=5)

Parameters

• func: This is a Python function or method representing the function to be integrated using the Gaussian quadrature. The function should accept vector inputs. When integrating a vector-valued function, the returned array must have the shape (..., len(x)).

• a: It is the lower limit of integration. It has the float type.

• b: It is the upper limit of integration. It has the float type.

• args: This is an optional parameter which is a sequence of extra arguments passed to func.

• n: This is the Gaussian quadrature’s order. The default value is $5$.

Return value

• val: This is the computed Gaussian quadrature approximation to the integral. It has the float type.

• none: This is the statistically returned value of None.

Code

Let’s see how to compute the Gaussian quadrature approximation of order $5$ of the function $f(x) = sin(x)$ using the scipy.integrate.fixed_quad method over the fixed interval $0- \pi/4$.

Explanation

• Line 1 and 2: We import the numpy library and the integrate sub-package from the scipy library.
• Line 4: We use the np.sin method in the NumPy library as our function to be integrated. We pass np.sin as the function and 0 and np.pi/4 as integration limits. $5$ is the order of the quadrature integration to the scipy.integrate.fixed_quad. We then print the result.