8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8f97853c-812f-4b7b-9d40-2de7a85886c0-18_563_853_274_566}
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\caption{Figure 3}
\end{figure}
Figure 3 shows part of the curve \(C\) with equation
$$y = \frac { 3 \ln \left( x ^ { 2 } + 1 \right) } { \left( x ^ { 2 } + 1 \right) } , \quad x \in \mathbb { R }$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
- Using your answer to (a), find the exact coordinates of the stationary point on the curve \(C\) for which \(x > 0\). Write each coordinate in its simplest form.
(4)
The finite region \(R\), shown shaded in Figure 3, is bounded by the curve \(C\), the \(x\)-axis and the line \(x = 3\) - Complete the table below with the value of \(y\) corresponding to \(x = 1\)
| \(x\) | 0 | 1 | 2 | 3 |
| \(y\) | 0 | | \(\frac { 3 } { 5 } \ln 5\) | \(\frac { 3 } { 10 } \ln 10\) |
- Use the trapezium rule with all the \(y\) values in the completed table to find an approximate value for the area of \(R\), giving your answer to 4 significant figures.
(2)