$($a$)(1$ point$)$ Jimmy is the first student to propose a solution.

Jimmy's attempt

The $\sqrt[\phantom{2}]{x}$ curve is above the $x-2$ line between $0$ and $4.$ The region starts at $x=0$ and ends at $x=4.$

That means its volume is:

$V={\displaystyle \underset{0}{\overset{4}{}}}[(\sqrt[\phantom{2}]{x}{)}^2-(x-2{)}^2]dx$

The main question why is jimmy is wrong. In at most a few sentences $($and some pictures, if you like$),$ explain the error$($s$)$ he is making.