2.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{e375f6ad-4a76-42a0-b7bf-ae47e5cbdaeb-04_479_855_310_566}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}

Figure 1 shows a sketch of the curve with equation $y = \mathrm { e } ^ { x } \sqrt { \sin x } , 0 \leqslant x \leqslant \pi$.

The finite region $R$, shown shaded in Figure 1, is bounded by the curve and the $x$-axis.
\begin{enumerate}[label=(\alph*)]
\item Complete the table below with the values of $y$ corresponding to $x = \frac { \pi } { 4 }$ and $x = \frac { \pi } { 2 }$, giving your answers to 5 decimal places.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$x$ & 0 & $\frac { \pi } { 4 }$ & $\frac { \pi } { 2 }$ & $\frac { 3 \pi } { 4 }$ & $\pi$ \\
\hline
$y$ & 0 &  &  & 8.87207 & 0 \\
\hline
\end{tabular}
\end{center}
\item Use the trapezium rule, with all the values of $y$ in the completed table, to obtain an estimate for the area of the region $R$. Give your answer to 4 decimal places.

The curve $y = \mathrm { e } ^ { x } \sqrt { \sin x } , 0 \leqslant x \leqslant \pi$, has a maximum turning point at $Q$, shown in Figure 1.
\item Find the $x$ coordinate of $Q$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel C34  Q2 [11]}}