OCR C4 2006 January — Question 6

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2006
SessionJanuary
TopicIntegration by Substitution
6
  1. Show that the substitution \(x = \sin ^ { 2 } \theta\) transforms \(\int \sqrt { \frac { x } { 1 - x } } \mathrm {~d} x\) to \(\int 2 \sin ^ { 2 } \theta \mathrm {~d} \theta\).
  2. Hence find \(\int _ { 0 } ^ { 1 } \sqrt { \frac { x } { 1 - x } } \mathrm {~d} x\).
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