#### Introduction

Continuing on the recently born series on numerical integration, this post will introduce rectangular integration. I will describe the concept behind rectangular integration, show a function in R for how to do it, and use it to check that the $latex Beta(2, 5)$ distribution actually integrates to 1 over its support set. This post follows from my previous post on trapezoidal integration.

Image courtesy of Qef from Wikimedia Commons.

#### Conceptual Background of Rectangular Integration (a.k.a. The Midpoint Rule)

Rectangular integration is a numerical integration technique that approximates the integral of a function with a rectangle. It uses rectangles to approximate the area under the curve. Here are its features:

- The rectangle’s
**width**is determined by the**interval of integration**.- One rectangle could span the width of the interval of integration and approximate the entire integral.
- Alternatively, the interval of integration could be sub-divided into…

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