Edexcel P3 2024 June — Question 6

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2024
SessionJune
TopicIntegration by Substitution

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 \(P ( 8,5 )\)
  1. 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 \(l\).
  2. Use algebraic integration to find the exact area of \(R\).