CAIE P3 2015 June — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2015
SessionJune
TopicIntegration by Parts

9
\includegraphics[max width=\textwidth, alt={}, center]{3eefd6c1-924c-4b7e-8d17-a2942fb48234-3_399_696_255_721} The diagram shows the curve \(y = x ^ { 2 } \mathrm { e } ^ { 2 - x }\) and its maximum point \(M\).
  1. Show that the \(x\)-coordinate of \(M\) is 2 .
  2. Find the exact value of \(\int _ { 0 } ^ { 2 } x ^ { 2 } \mathrm { e } ^ { 2 - x } \mathrm {~d} x\).