7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{582cda45-80fc-43a8-90e6-1cae08cb1534-12_563_812_244_630}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of part of the curve with equation
$$y = 3 x - x ^ { \frac { 3 } { 2 } } , \quad x \geqslant 0$$
The finite region \(S\), bounded by the \(x\)-axis and the curve, is shown shaded in Figure 3.
- Find
$$\int \left( 3 x - x ^ { \frac { 3 } { 2 } } \right) \mathrm { d } x$$
- Hence find the area of \(S\).