CAIE P3 2014 June — Question 8

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2014
SessionJune
TopicIntegration with Partial Fractions

8 Let \(f ( x ) = \frac { 6 + 6 x } { ( 2 - x ) \left( 2 + x ^ { 2 } \right) }\).
  1. Express \(\mathrm { f } ( x )\) in the form \(\frac { A } { 2 - x } + \frac { B x + C } { 2 + x ^ { 2 } }\).
  2. Show that \(\int _ { - 1 } ^ { 1 } \mathrm { f } ( x ) \mathrm { d } x = 3 \ln 3\).