OCR C4 2009 June — Question 6

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2009
SessionJune
TopicPartial Fractions
TypeRepeated factor with distinct linear factors

6 The expression \(\frac { 4 x } { ( x - 5 ) ( x - 3 ) ^ { 2 } }\) is denoted by \(\mathrm { f } ( x )\).
  1. Express f \(( x )\) in the form \(\frac { A } { x - 5 } + \frac { B } { x - 3 } + \frac { C } { ( x - 3 ) ^ { 2 } }\), where \(A , B\) and \(C\) are constants.
  2. Hence find the exact value of \(\int _ { 1 } ^ { 2 } \mathrm { f } ( x ) \mathrm { d } x\).