Integrating functions numerically using SciPy

Integration can be interpreted as the area that lies between a curve and the axis, signed according to whether this area is above or below the axis. Some integrals cannot be computed directly using symbolic means, and instead, have to be approximated numerically. One classic example of this is the Gaussian error function, which was mentioned in the Understanding basic mathematical functions section in Chapter 1, An Introduction to Basic Packages, Functions, and Concepts. This is defined by the following formula:

Furthermore, the integral that appears here cannot be evaluated symbolically.

In this recipe, we will see how to use numerical integration routines in the SciPy package to compute the integral of a function.

Getting ready

We use the scipy.integrate module, which contains several routines for computing numerical integrals. We also import the NumPy library as np. We import this module as follows...