CAIE P3 2022 November — Question 10

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2022
SessionNovember
TopicIntegration with Partial Fractions

10 Let \(\mathrm { f } ( x ) = \frac { 4 - x + x ^ { 2 } } { ( 1 + x ) \left( 2 + x ^ { 2 } \right) }\).
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Find the exact value of \(\int _ { 0 } ^ { 4 } \mathrm { f } ( x ) \mathrm { d } x\). Give your answer as a single logarithm.
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