By writing \(\tan x\) as \(\frac { \sin x } { \cos x }\), use the quotient rule to show that \(\frac { \mathrm { d } } { \mathrm { d } x } ( \tan x ) = \sec ^ { 2 } x\). [0pt]
[2 marks]
Use integration by parts to find \(\int x \sec ^ { 2 } x \mathrm {~d} x\). [0pt]
[4 marks]
The region bounded by the curve \(y = ( 5 \sqrt { x } ) \sec x\), the \(x\)-axis from 0 to 1 and the line \(x = 1\) is rotated through \(2 \pi\) radians about the \(x\)-axis to form a solid.
Find the value of the volume of the solid generated, giving your answer to two significant figures. [0pt]
[3 marks]