8 Fig. 8 shows part of the curve \(y = x \cos 3 x\).
The curve crosses the \(x\)-axis at \(\mathrm { O } , \mathrm { P }\) and Q .
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\includegraphics[alt={},max width=\textwidth]{3b3e20ee-457c-46be-b2e5-12573bee2fbf-3_551_1189_925_479}
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\caption{Fig. 8}
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- Find the exact coordinates of P and Q .
- Find the exact gradient of the curve at the point P .
Show also that the turning points of the curve occur when \(x \tan 3 x = \frac { 1 } { 3 }\).
- Find the area of the region enclosed by the curve and the \(x\)-axis between O and P , giving your answer in exact form.