AQA C2 2005 January — Question 4

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2005
SessionJanuary
TopicIndefinite & Definite Integrals
4
  1. Write \(\sqrt { x }\) in the form \(x ^ { k }\), where \(k\) is a fraction.
  2. Hence express \(\sqrt { x } ( x - 1 )\) in the form \(x ^ { p } - x ^ { q }\).
  3. Find \(\int \sqrt { x } ( x - 1 ) \mathrm { d } x\).
  4. Hence show that \(\int _ { 1 } ^ { 2 } \sqrt { x } ( x - 1 ) \mathrm { d } x = \frac { 4 } { 15 } ( \sqrt { 2 } + 1 )\).
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