OCR FP2 2010 June — Question 5

Exam BoardOCR
ModuleFP2 (Further Pure Mathematics 2)
Year2010
SessionJune
TopicReduction Formulae

5 It is given that, for \(n \geqslant 0\), $$I _ { n } = \int _ { 0 } ^ { \frac { 1 } { 2 } } ( 1 - 2 x ) ^ { n } \mathrm { e } ^ { x } \mathrm {~d} x$$
  1. Prove that, for \(n \geqslant 1\), $$I _ { n } = 2 n I _ { n - 1 } - 1$$
  2. Find the exact value of \(I _ { 3 }\).