2 In this question you must show detailed reasoning.
Show that \(\int _ { 5 } ^ { \infty } ( x - 1 ) ^ { - \frac { 3 } { 2 } } \mathrm {~d} x = 1\).
\(3 A\) is a fixed point on a smooth horizontal surface. A particle \(P\) is initially held at \(A\) and released from rest. It subsequently performs simple harmonic motion in a straight line on the surface. After its release it is next at rest after 0.2 seconds at point \(B\) whose displacement is 0.2 m from \(A\). The point \(M\) is halfway between \(A\) and \(B\). The displacement of \(P\) from \(M\) at time \(t\) seconds after release is denoted by \(x \mathrm {~m}\).

1. Sketch a graph of \(x\) against \(t\) for \(0 \leqslant t \leqslant 0.4\).
2. Find the displacement of \(P\) from \(M\) at 0.75 seconds after release.