Use Simpson's rule with four strips to find an approximation to
$$\int _ { 0 } ^ { 2 } \mathrm { e } ^ { \sqrt { x } } \mathrm {~d} x$$
giving your answer correct to 3 significant figures.
Deduce an approximation to \(\int _ { 0 } ^ { 2 } \left( 1 + 10 \mathrm { e } ^ { \sqrt { x } } \right) \mathrm { d } x\).