Edexcel FP3 2017 June — Question 8

Exam BoardEdexcel
ModuleFP3 (Further Pure Mathematics 3)
Year2017
SessionJune
TopicHyperbolic functions

8. The curve \(C\) has equation $$y = \ln \left( \frac { \mathrm { e } ^ { x } + 1 } { \mathrm { e } ^ { x } - 1 } \right) , \quad \ln 2 \leqslant x \leqslant \ln 3$$
  1. Show that $$\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 2 \mathrm { e } ^ { x } } { \mathrm { e } ^ { 2 x } - 1 }$$
  2. Find the length of the curve \(C\), giving your answer in the form \(\ln a\), where \(a\) is a rational number.
    (6)