8 The function g is defined by
$$\mathrm { g } ( x ) = \mathrm { e } ^ { \sin x } \quad ( 0 \leq x \leq 2 \pi )$$
The diagram below shows the graph of \(y = \mathrm { g } ( x )\)
\includegraphics[max width=\textwidth, alt={}, center]{a9f88195-e545-43f2-a13a-6459d14e1cda-09_369_593_548_721}
8
- Find the \(x\)-coordinate of each of the stationary points of the graph of \(y = \mathrm { g } ( x )\), giving your answers in exact form.
8
- Use Simpson's rule with 3 ordinates to estimate
$$\int _ { 0 } ^ { \pi } g ( x ) d x$$
giving your answer to two decimal places.
8 - Explain how Simpson's rule could be used to find a more accurate estimate of the integral in part (b).