CAIE P3 2024 November — Question 11

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2024
SessionNovember
TopicIntegration by Substitution

11
\includegraphics[max width=\textwidth, alt={}, center]{6280ab81-0bdb-47b4-8651-bff1261a0adf-18_565_634_260_717} The diagram shows the curve \(y = 2 \sin x \sqrt { 2 + \cos x }\), for \(0 \leqslant x \leqslant 2 \pi\), and its minimum point \(M\), where \(x = a\).
  1. Find the value of \(a\) correct to 2 decimal places.
    \includegraphics[max width=\textwidth, alt={}, center]{6280ab81-0bdb-47b4-8651-bff1261a0adf-18_2716_38_109_2012}
    \includegraphics[max width=\textwidth, alt={}, center]{6280ab81-0bdb-47b4-8651-bff1261a0adf-19_2726_33_97_22}
  2. Use the substitution \(u = 2 + \cos x\) to find the exact area of the shaded region \(R\).
    If you use the following page to complete the answer to any question, the question number must be clearly shown.