Numerical integration is integration using numerical methods instead of analytical methods. SciPy has a numerical integration package, scipy.integrate, which has no equivalent in NumPy. The quad function can integrate a one-variable function between two points. These points can be at infinity.

The Gaussian integral is related to the error function, but has no finite limits. It evaluates to the square root of pi. Let's calculate the Gaussian integral with the quad function as shown in the following line of code:

print "Gaussian integral", np.sqrt(np.pi),integrate.quad(lambda x: np.exp(-x**2), -np.inf, np.inf)

The return value is the outcome, and its error would be:

Gaussian integral 1.77245385091 (1.7724538509055159, 1.4202636780944923e-08)