13.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ace492d8-1dd0-401e-af74-505ca19d5e9c-28_583_917_155_676}
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\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of the curve \(C\) with parametric equations
$$x = \ln ( t + 2 ) , y = \frac { 1 } { t + 1 } , \quad t > - \frac { 2 } { 3 }$$
- State the domain of values of \(x\) for the curve \(C\).
The finite region \(R\), shown shaded in Figure 4, is bounded by the curve \(C\), the line with equation \(x = \ln 2\), the \(x\)-axis and the line with equation \(x = \ln 4\)
- Use calculus to show that the area of \(R\) is \(\ln \left( \frac { 3 } { 2 } \right)\).
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