Use the substitution \(u=\sqrt{x-2}\) to find \(\int x\sqrt{x-2}\ dx\).[4]
Two curves \(C_1\) and \(C_2\) have equations \(y=x\sqrt{x-2}\) and \(y=\frac{1}{x^2-1}\) respectively.
Find the exact area enclosed by \(C_1\), \(C_2\) and the lines \(x=3\) and \(x=6\).[3]
The region in part (b) is rotated about the \(x\)-axis through \(360^\circ\). Find the volume generated, leaving your answer in 2 decimal places.[2]