AQA
Paper 3
2024
June
Q11
10 marks
11 The curve \(C\) with equation
$$y = \left( x ^ { 2 } - 8 x \right) \ln x$$
is defined for \(x > 0\) and is shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{deec0d32-b031-4227-bc80-7150a0acbc94-20_862_632_502_767}
The shaded region, \(R\), lies below the \(x\)-axis and is bounded by \(C\) and the \(x\)-axis.
Show that the area of \(R\) can be written as
$$p + q \ln 2$$
where \(p\) and \(q\) are rational numbers to be found.
[0pt]
[10 marks]
\section*{END OF SECTION A}