- (i) Given that
$$\int _ { 1 } ^ { 3 } \left( x ^ { 2 } - 2 x + k \right) d x = 8 \frac { 2 } { 3 }$$
find the value of the constant \(k\).
(ii) Evaluate
$$\int _ { 2 } ^ { \infty } \frac { 6 } { x ^ { \frac { 5 } { 2 } } } \mathrm {~d} x$$
giving your answer in its simplest form.