Area with logarithmic functions

A question is this type if and only if the curve equation involves logarithmic functions (ln x or log x) and requires integration techniques specific to logarithms.

2 questions · Standard +0.2

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OCR MEI Paper 1 2018 June Q10

8 marks Challenging +1.2

10 Fig. 10 shows the graph of \(y = ( k - x ) \ln x\) where \(k\) is a constant ( \(k > 1\) ). \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{904025c9-6d68-4344-bd41-8c0fccfcf92f-06_454_1266_1564_395} \captionsetup{labelformat=empty} \caption{Fig. 10}

\end{figure} Find, in terms of \(k\), the area of the finite region between the curve and the \(x\)-axis.

OCR H240/02 2023 June Q3

3 marks Moderate -0.8

In this question you must show detailed reasoning. Find the exact area of the region enclosed by the curve \(y = \frac{1}{x+2}\), the two axes and the line \(x = 2.5\). [3]