6. (a) Find
$$\int 10 x \left( x ^ { \frac { 1 } { 2 } } - 2 \right) \mathrm { d } x$$
giving each term in its simplest form.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8a7593c3-4f0b-4351-afae-7bd98cfc351d-10_401_1002_543_470}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the curve \(C\) with equation
$$y = 10 x \left( x ^ { \frac { 1 } { 2 } } - 2 \right) , \quad x \geqslant 0$$
The curve \(C\) starts at the origin and crosses the \(x\)-axis at the point \(( 4,0 )\).
The area, shown shaded in Figure 2, consists of two finite regions and is bounded by the curve \(C\), the \(x\)-axis and the line \(x = 9\)
(b) Use your answer from part (a) to find the total area of the shaded regions.