CAIE P3 2003 November — Question 8

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2003
SessionNovember
TopicIntegration with Partial Fractions

8 Let \(\mathrm { f } ( x ) = \frac { x ^ { 3 } - x - 2 } { ( x - 1 ) \left( x ^ { 2 } + 1 \right) }\).
  1. Express \(\mathrm { f } ( x )\) in the form $$A + \frac { B } { x - 1 } + \frac { C x + D } { x ^ { 2 } + 1 }$$ where \(A , B , C\) and \(D\) are constants.
  2. Hence show that \(\int _ { 2 } ^ { 3 } \mathrm { f } ( x ) \mathrm { d } x = 1\).