By using integration by parts twice, find
$$\int x ^ { 2 } \sin 2 x d x$$
A curve has equation \(y = x \sqrt { \sin 2 x }\), for \(0 \leqslant x \leqslant \frac { \pi } { 2 }\).
The region bounded by the curve and the \(x\)-axis is rotated through \(2 \pi\) radians about the \(x\)-axis to generate a solid.
Find the exact value of the volume of the solid generated. [0pt]
[3 marks]