Edexcel C34 2014 June — Question 9

Exam BoardEdexcel
ModuleC34 (Core Mathematics 3 & 4)
Year2014
SessionJune
TopicArea Under & Between Curves

9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{423eb549-0873-4185-8faf-12dedafcd108-13_849_841_214_571} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of part of the curve with equation \(y = \mathrm { e } ^ { \sqrt { x } } , x > 0\)
The finite region \(R\), shown shaded in Figure 1, is bounded by the curve, the \(x\)-axis and the lines \(x = 4\) and \(x = 9\)
  1. Use the trapezium rule, with 5 strips of equal width, to obtain an estimate for the area of \(R\), giving your answer to 2 decimal places.
  2. Use the substitution \(u = \sqrt { x }\) to find, by integrating, the exact value for the area of \(R\).