Edexcel AEA 2003 June — Question 3

Exam BoardEdexcel
ModuleAEA (Advanced Extension Award)
Year2003
SessionJune
TopicParametric equations

3. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{25f0c7cc-0701-4836-931e-0eff5145e029-2_441_1111_1598_551}
\end{figure} Figure 2 shows a sketch of a part of the curve \(C\) with parametric equations $$x = t ^ { 3 } , y = t ^ { 2 } .$$ The tangent at the point \(P ( 8,4 )\) cuts \(C\) at the point \(Q\) .
Find the area of the shaded region between \(P Q\) and \(C\) .