Exact area with surds

\includegraphics[alt={},max width=\textwidth]{d37eaba2-0a25-4abf-b2c8-1e08673229fb-14_1090_1205_274_456} \captionsetup{labelformat=empty} \caption{Figure 2
Figure 2 shows a sketch of part of the curve with equation $$y = \frac { 12 x - x ^ { 2 } } { \sqrt { x } } , \quad x > 0$$ The region \(R\), shows shaded in figure 2, is bounded by the curve, the line with equation \(x = 4\), the \(x\)-axis and the line with equation \(x = 8\).
Show that the area of the shaded region \(R\) is \(\frac { 128 } { 5 } ( 3 \sqrt { 2 } - 2 )\).}

\includegraphics[alt={},max width=\textwidth]{089f5506-94ac-489f-b219-e67fa6ca834f-4_536_883_248_486} \captionsetup{labelformat=empty} \caption{Figure 3}