This page, like many others on this site, is under major construction. Right now, it pretty much just consists of my lecture notes.

**W**hile we have been able to integrate some pretty interesting-looking functions so far, the sad reality is that there are far more functions that we can

*not*evaluate analytically (i.e., by hand) due to the fact that there is no closed form representation for their antiderivative. Moreover, those of you who are destined to pursue careers in science will find out soon enough that you rarely are given pretty functions to integrate. Instead, you are dealing with large sets of discrete data points. What do we do in these situations?

Fortunately, we previously developed some methods which allow us to

*approximate*the value of integrals. This process of

*approximating*the value of an integral is called

**numerical integration**

*.*

**DEFINITION | Numerical integration**

**Numerical integration**, also known as

**numerical quadrature**, is the process of using sample points (discrete points) instead of a continuous interval to approximate the value of a definite integral.

Numerical integration is a massive topic in numerical analysis (one of the many sub-fields of mathematics). While the most common numerical integration techniques taught in integral calculus are the endpoint, midpoint, trapezoidal, and Simpson's methods, there are scores of others that yet await the curious soul.