3 The definite integral \(I\) is defined by \(I = \int _ { 0 } ^ { 2 } \left( 4 \mathrm { e } ^ { \frac { 1 } { 2 } x } + 3 \right) \mathrm { d } x\).
- Show that \(I = 8 \mathrm { e } - 2\).
- Sketch the curve \(y = 4 \mathrm { e } ^ { \frac { 1 } { 2 } x } + 3\) for \(0 \leqslant x \leqslant 2\).
- State whether an estimate of \(I\) obtained by using the trapezium rule will be more than or less than \(8 \mathrm { e } - 2\). Justify your answer.