7
\includegraphics[max width=\textwidth, alt={}, center]{9d93ad8c-0a22-4de7-8342-387606e4e510-3_584_675_945_735} The diagram shows the part of the curve \(y = \mathrm { e } ^ { x } \cos x\) for \(0 \leqslant x \leqslant \frac { 1 } { 2 } \pi\). The curve meets the \(y\)-axis at the point \(A\). The point \(M\) is a maximum point.

1. Write down the coordinates of \(A\).
2. Find the \(x\)-coordinate of \(M\).
3. Use the trapezium rule with three intervals to estimate the value of $$\int _ { 0 } ^ { \frac { 1 } { 2 } \pi } e ^ { x } \cos x d x$$ giving your answer correct to 2 decimal places.
4. State, with a reason, whether the trapezium rule gives an under-estimate or an over-estimate of the true value of the integral in part (iii).