2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{63249f82-4eab-47bc-aeae-3af8ec737b51-2_499_828_651_621}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows part of the curve with equation \(y = 2 \cosh \left( \frac { 1 } { 2 } x \right)\). The points \(A\) and \(B\) lie on the curve and have \(x\)-coordinates \(- \ln 2\) and \(\ln 2\) respectively. The arc of the curve joining \(A\) and \(B\) is rotated through \(2 \pi\) radians about the \(x\)-axis.
Find the exact area of the curved surface area formed.
(Total 7 marks)