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\includegraphics[max width=\textwidth, alt={}, center]{ae57d8f1-5a0d-426c-952d-e8b99c6aeaba-5_609_897_255_625}
The diagram shows part of the curve \(y = \frac { 1 } { ( 3 x + 1 ) ^ { \frac { 1 } { 4 } } }\). The curve cuts the \(y\)-axis at \(A\) and the line \(x = 5\) at \(B\).
- Show that the equation of the line \(A B\) is \(y = - \frac { 1 } { 10 } x + 1\).
- Find the volume obtained when the shaded region is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.