CAIE P3 2005 November — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2005
SessionNovember
TopicIntegration by Substitution
6
  1. Use the substitution \(x = \sin ^ { 2 } \theta\) to show that $$\int \sqrt { } \left( \frac { x } { 1 - x } \right) \mathrm { d } x = \int 2 \sin ^ { 2 } \theta \mathrm {~d} \theta$$
  2. Hence find the exact value of $$\left. \int _ { 0 } ^ { \frac { 1 } { 4 } } \sqrt { ( } \frac { x } { 1 - x } \right) \mathrm { d } x$$
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