\(\quad \int x \cos 4 x \mathrm {~d} x\);
(4 marks)
\(\int x ^ { 2 } \sin 4 x d x\).
(4 marks)
The region bounded by the curve \(y = 8 x \sqrt { ( \sin 4 x ) }\) and the lines \(x = 0\) and \(x = 0.2\) is rotated through \(2 \pi\) radians about the \(x\)-axis. Find the value of the volume of the solid generated, giving your answer to three significant figures.
(3 marks)