6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f07cc9ed-a820-46c8-a3a3-3c780cf20fa7-09_796_1132_121_397}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of part of the curve \(C\) with equation
$$y = \frac { 1 } { 8 } x ^ { 3 } + \frac { 3 } { 4 } x ^ { 2 } , \quad x \in \mathbb { R }$$
The curve \(C\) has a maximum turning point at the point \(A\) and a minimum turning point at the origin \(O\).
The line \(l\) touches the curve \(C\) at the point \(A\) and cuts the curve \(C\) at the point \(B\).
The \(x\) coordinate of \(A\) is - 4 and the \(x\) coordinate of \(B\) is 2 .
The finite region \(R\), shown shaded in Figure 3, is bounded by the curve \(C\) and the line \(l\).
Use integration to find the area of the finite region \(R\).