Split an absolute integral at the sign change

The curve $C$ is $y=x\cos2x$, $0\le x\le\pi$.

(i) Find its exact x-axis intercepts.3 marks

(ii) Sketch $C$, stating all x- and y-axis intercept coordinates.2 marks

(iii) Find the exact value of $\int_{\pi/4}^\pi|x\cos2x|\,dx$.4 marks

(iv) Find the volume when the region bounded by $C$, the x-axis and $x=\pi$ rotates completely about the x-axis.2 marks