AQA FP3 2010 June — Question 3

Exam BoardAQA
ModuleFP3 (Further Pure Mathematics 3)
Year2010
SessionJune
TopicIntegration with Partial Fractions
3
  1. Explain why \(\int _ { 1 } ^ { \infty } 4 x \mathrm { e } ^ { - 4 x } \mathrm {~d} x\) is an improper integral.
  2. Find \(\quad \int 4 x \mathrm { e } ^ { - 4 x } \mathrm {~d} x\).
  3. Hence evaluate \(\int _ { 1 } ^ { \infty } 4 x \mathrm { e } ^ { - 4 x } \mathrm {~d} x\), showing the limiting process used.
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