AQA FP3 2008 June — Question 5

Exam BoardAQA
ModuleFP3 (Further Pure Mathematics 3)
Year2008
SessionJune
TopicIntegration by Parts
5
  1. Find \(\int x ^ { 3 } \ln x \mathrm {~d} x\).
  2. Explain why \(\int _ { 0 } ^ { \mathrm { e } } x ^ { 3 } \ln x \mathrm {~d} x\) is an improper integral.
  3. Evaluate \(\int _ { 0 } ^ { \mathrm { e } } x ^ { 3 } \ln x \mathrm {~d} x\), showing the limiting process used.
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