14.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ea81408b-e292-4529-b1e2-e3246503a3ac-21_641_920_260_568}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
The finite region \(R\), which is shown shaded in Figure 3, is bounded by the straight line \(l\) with equation \(y = 4 x + 3\) and the curve \(C\) with equation \(y = 2 x ^ { \frac { 3 } { 2 } } - 2 x + 3 , x \geqslant 0\)
The line \(l\) meets the curve \(C\) at the point \(A\) on the \(y\)-axis and \(l\) meets \(C\) again at the point \(B\), as shown in Figure 3.
- Use algebra to find the coordinates of \(A\) and \(B\).
- Use integration to find the area of the shaded region \(R\).