OCR C4 2011 January — Question 2

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2011
SessionJanuary
TopicPartial Fractions
TypeRepeated factor with distinct linear factors

2
  1. Express \(\frac { 7 - 2 x } { ( x - 2 ) ^ { 2 } }\) in the form \(\frac { A } { x - 2 } + \frac { B } { ( x - 2 ) ^ { 2 } }\), where \(A\) and \(B\) are constants.
  2. Hence find the exact value of \(\int _ { 4 } ^ { 5 } \frac { 7 - 2 x } { ( x - 2 ) ^ { 2 } } \mathrm {~d} x\).