CAIE P3 2012 June — Question 8

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2012
SessionJune
TopicIntegration with Partial Fractions

8 Let \(\mathrm { f } ( x ) = \frac { 4 x ^ { 2 } - 7 x - 1 } { ( x + 1 ) ( 2 x - 3 ) }\).
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Show that \(\int _ { 2 } ^ { 6 } \mathrm { f } ( x ) \mathrm { d } x = 8 - \ln \left( \frac { 49 } { 3 } \right)\).