CAIE P2 2014 November — Question 5

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2014
SessionNovember
TopicChain Rule

5
\includegraphics[max width=\textwidth, alt={}, center]{c703565b-8aa8-424b-9684-6592d4effdf8-2_554_689_1354_726} The diagram shows part of the curve $$y = 2 \cos x - \cos 2 x$$ and its maximum point \(M\). The shaded region is bounded by the curve, the axes and the line through \(M\) parallel to the \(y\)-axis.
  1. Find the exact value of the \(x\)-coordinate of \(M\).
  2. Find the exact value of the area of the shaded region.