AQA FP3 2006 January — Question 2

Exam BoardAQA
ModuleFP3 (Further Pure Mathematics 3)
Year2006
SessionJanuary
TopicIntegration by Parts
2
  1. Find \(\int _ { 0 } ^ { a } x \mathrm { e } ^ { - 2 x } \mathrm {~d} x\), where \(a > 0\).
  2. Write down the value of \(\lim _ { a \rightarrow \infty } a ^ { k } \mathrm { e } ^ { - 2 a }\), where \(k\) is a positive constant.
  3. Hence find \(\int _ { 0 } ^ { \infty } x \mathrm { e } ^ { - 2 x } \mathrm {~d} x\).
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