5 It is given that, for non-negative integers \(n\),
$$I _ { n } = \int _ { 0 } ^ { \frac { 1 } { 2 } \pi } x ^ { n } \cos x \mathrm {~d} x$$
- Prove that, for \(n \geqslant 2\),
$$I _ { n } = \left( \frac { 1 } { 2 } \pi \right) ^ { n } - n ( n - 1 ) I _ { n - 2 } .$$
- Find \(I _ { 4 }\) in terms of \(\pi\).