CAIE P3 2015 June — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2015
SessionJune
TopicIntegration by Substitution

6 Let \(I = \int _ { 0 } ^ { 1 } \frac { \sqrt { } x } { 2 - \sqrt { } x } \mathrm {~d} x\).
  1. Using the substitution \(u = 2 - \sqrt { } x\), show that \(I = \int _ { 1 } ^ { 2 } \frac { 2 ( 2 - u ) ^ { 2 } } { u } \mathrm {~d} u\).
  2. Hence show that \(I = 8 \ln 2 - 5\).