8 The definite integral \(I\) is defined by
$$I = \int _ { 0 } ^ { 6 } 2 ^ { x } \mathrm {~d} x$$
- Use Simpson's rule with 6 strips to find an approximate value of \(I\).
- By first writing \(2 ^ { x }\) in the form \(\mathrm { e } ^ { k x }\), where the constant \(k\) is to be determined, find the exact value of \(I\).
- Use the answers to parts (i) and (ii) to deduce that \(\ln 2 \approx \frac { 9 } { 13 }\).