\(\quad\) Find \(\int t \cos \left( \frac { \pi } { 4 } t \right) \mathrm { d } t\).
The platform of a theme park ride oscillates vertically. For the first 75 seconds of the ride,
$$\frac { \mathrm { d } x } { \mathrm {~d} t } = \frac { t \cos \left( \frac { \pi } { 4 } t \right) } { 32 x }$$
where \(x\) metres is the height of the platform above the ground after time \(t\) seconds.
At \(t = 0\), the height of the platform above the ground is 4 metres.
Find the height of the platform after 45 seconds, giving your answer to the nearest centimetre.
(6 marks)