6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5a695b86-1660-4c06-ac96-4cdb07af9a2e-18_856_990_246_539}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Figure 3 shows a sketch of part of the curve with equation
$$y = \sqrt { 4 x - 7 }$$
The line \(l\), shown in Figure 3, is the normal to the curve at the point \(P ( 8,5 )\)
- Use calculus to show that an equation of \(l\) is
$$5 x + 2 y - 50 = 0$$
The region \(R\), shown shaded in Figure 3, is bounded by the curve, the \(x\)-axis and \(l\).
- Use algebraic integration to find the exact area of \(R\).