CAIE P3 2011 November — Question 8

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2011
SessionNovember
TopicIntegration with Partial Fractions

8 Let \(f ( x ) = \frac { 12 + 8 x - x ^ { 2 } } { ( 2 - x ) \left( 4 + x ^ { 2 } \right) }\).
  1. Express \(\mathrm { f } ( x )\) in the form \(\frac { A } { 2 - x } + \frac { B x + C } { 4 + x ^ { 2 } }\).
  2. Show that \(\int _ { 0 } ^ { 1 } \mathrm { f } ( x ) \mathrm { d } x = \ln \left( \frac { 25 } { 2 } \right)\).