Answer
$5.25$
Work Step by Step
Let us consider $R_n$ be the approximation obtained by using $n$ rectangles of same width.
The exact area can be found under the graph of $f$:
$A=\lim\limits_{n\to \infty} f(x_k)\triangle x$; where $\triangle x=\dfrac{b-a}{n}$
Given: $f(x)=\dfrac{x}{2}+2$
Here, we have $\triangle x=\dfrac{b-a}{n}=\dfrac{2-0}{4}=0.5$
$A=\lim\limits_{n\to \infty} f(x_k)\triangle x$
or, $A=[f(x_1)+f(x_2)+f(x_3)+f(x_4)]\triangle x$
or, $A=[(\dfrac{0.5}{2})+2+(\dfrac{1}{2})+2+(\dfrac{1.5}{2})+(\dfrac{2}{2})](0.5)$
Thus, $A=5.25$
