Computing integrals using a Gaussian quadrature

In the next sections, we will look at how to compute integrals in detail.

Getting ready

This recipe can be done by using the following integration equations.

• quad: General-purpose integration
• dblquad: General-purpose double integration
• tplquad: General-purpose triple integration
• fixed_quad: Integrate func(x) using Gaussian quadrature of order n
• quadrature: Integrate with the given tolerance using Gaussian quadrature
• romberg: Integrate func using Romberg integration

How to do it...

There are other possibilities is to use Gaussian quadrature formulas, they are:

• These are more powerful, since the accuracy of the approximations is gained through internally computing the best possible choice of nodes
• There are two basic routines in the scipy.integrate module that perform the implementation of this algorithm: quadrature, if we want to specify tolerance, or fixed_quad, if we wish to specify the number of nodes (but not their locations!):

In [38]: from scipy.integrate...