AQA FP3 2008 January — Question 4

Exam BoardAQA
ModuleFP3 (Further Pure Mathematics 3)
Year2008
SessionJanuary
TopicIntegration with Partial Fractions
4
  1. Explain why \(\int _ { 1 } ^ { \infty } x \mathrm { e } ^ { - 3 x } \mathrm {~d} x\) is an improper integral.
  2. Find \(\int x \mathrm { e } ^ { - 3 x } \mathrm {~d} x\).
  3. Hence evaluate \(\int _ { 1 } ^ { \infty } x \mathrm { e } ^ { - 3 x } \mathrm {~d} x\), showing the limiting process used.
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