Question

Let $R=\left\{\right(x,y)\mid a\le x\le b\text{and}c\le y\le d\}$be a rectangular region. Explain why R is both a type I region and a type II region.

Short answer

The region may be considered as either type I or type II region.

Step-by-step solution

Given Information

It is given that $R=\left\{\right(x,y)\mid a\le x\le b\text{and}c\le y\le d\}$

Determining type I region

It is observed that for values of $x$in $[a,b]$, the function $y=c$and $y=d$are such that $c<d$

Hence, region is bounded by $y=c\text{, above by}y=d\text{,}$left by $x=a$and right by $x=b$

Region is type I.

Determining type II region

For all values of $y$in interval $[c,d]$, the functions $x=a,x=b$are such that $a<b$.

Hence, region is bounded below by $y=c\text{, above by}y=d\text{,}$left by $x=a$and right by $x=b$

Region is type II region.