- The curve \(C\) has equation
$$y = \arccos \left( \frac { 1 } { 2 } x \right) \quad - 2 \leqslant x \leqslant 2$$
- Show that \(C\) has no stationary points.
The normal to \(C\), at the point where \(x = 1\), crosses the \(x\)-axis at the point \(A\) and crosses the \(y\)-axis at the point \(B\).
Given that \(O\) is the origin,
- show that the area of the triangle \(O A B\) is \(\frac { 1 } { 54 } \left( p \sqrt { 3 } + q \pi + r \sqrt { 3 } \pi ^ { 2 } \right)\) where \(p\), \(q\) and \(r\) are integers to be determined.
(5)