CAIE FP1 2011 November — Question 9

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionNovember
TopicHyperbolic functions

9 The curve \(C\) has equation \(y = \frac { 1 } { 2 } \left( \mathrm { e } ^ { x } + \mathrm { e } ^ { - x } \right)\) for \(0 \leqslant x \leqslant \ln 5\). Find
  1. the mean value of \(y\) with respect to \(x\) over the interval \(0 \leqslant x \leqslant \ln 5\),
  2. the arc length of \(C\),
  3. the surface area generated when \(C\) is rotated through \(2 \pi\) radians about the \(x\)-axis.