General Regions in 2D

Definition: General Region in \(\mathbb{R}^2\)

A general region of in \(\mathbb{R}^2\) is a subset \(D\subseteq\mathbb{R}^2\) which can be described in one of the following ways for two real numbers \(a,b\) and two continuous real functions \(l,u: [a;b] \to \mathbb{R}\):

• Type I: \(D = \{(x,y) \mid a\le x\le b, l(x) \le y \le u(x)\}\)
• Type II: \(D = \{(x,y) \mid l(y) \le x \le u(y), a \le y \le b\}\)