- Given that
$$I _ { n } = \int _ { 0 } ^ { 4 } x ^ { n } \sqrt { } \left( 16 - x ^ { 2 } \right) \mathrm { d } x , \quad n \geqslant 0$$
- prove that, for \(n \geqslant 2\),
$$( n + 2 ) I _ { n } = 16 ( n - 1 ) I _ { n - 2 }$$
- Hence, showing each step of your working, find the exact value of \(I _ { 5 }\)