SPS SPS FM 2022 November — Question 5

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2022
SessionNovember
TopicHyperbolic functions

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{657b12c4-cab7-4fc1-9481-94131aeeb6b9-12_595_1579_194_274} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} The curves in Figure 1 have equations $$y = 6 \cosh ( x ) \text { and } y = 9 - 2 \sinh ( x )$$
  1. Find exact values for the \(x\)-coordinates of the two points where the curves intersect. The finite region between the two curves is shaded in Figure 1.
  2. Using calculus, find the area of the shaded region, giving your answer in the form \(a \ln ( b ) + c\), where \(a , b\) and \(c\) are integers.
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