Answer
Matches $(a)$
Work Step by Step
Given $$f(x)= 2-\frac{x}{2}, \ g(x)=2-\sqrt {x}$$
To determine the area between the curves $f(x)= 2-\frac{x}{2}, \ g(x)=2-\sqrt {x}$
frist we get the intersection points, by solving the following equations
$y= 2-\frac{x}{2}, \ y=2-\sqrt {x}$
we get $(0,2),(4,0)$
So,
\begin{align}
A&=\int_ 0^4 (2-\frac{x}{2}-(2-\sqrt {x})) \ dx \\
&=\left[ -\frac{x^2}{4}+\frac{2x^\frac{3}{2}}{3}\right]_0^3\\
&=\frac{4}{3}\approx 1
\end{align}
