4. \(\quad I _ { n } = \int _ { 0 } ^ { a } ( a - x ) ^ { n } \cos x \mathrm {~d} x , \quad a > 0 , \quad n \geqslant 0\)
- Show that, for \(n \geqslant 2\),
$$I _ { n } = n \tilde { a } ^ { - 1 } - n ( n - 1 ) I _ { n - 2 }$$
- Hence evaluate \(\int _ { 0 } ^ { \frac { \pi } { 2 } } \left( \frac { \pi } { 2 } - x \right) ^ { 2 } \cos x \mathrm {~d} x\).