6. (a) Find \(\int \sqrt { } ( 5 - x ) \mathrm { d } x\).
(2)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c2622c33-9436-4254-a728-10ba4703a28c-11_503_1270_370_335}
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\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of the curve with equation
$$y = ( x - 1 ) \sqrt { } ( 5 - x ) , \quad 1 \leqslant x \leqslant 5$$
(b) (i) Using integration by parts, or otherwise, find
$$\int ( x - 1 ) \sqrt { } ( 5 - x ) \mathrm { d } x$$
(ii) Hence find \(\int _ { 1 } ^ { 5 } ( x - 1 ) \sqrt { } ( 5 - x ) \mathrm { d } x\).