5.
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The diagram shows the curve with equation \(y = \frac { 1 } { \sqrt { 3 x + 1 } }\).
The shaded region is bounded by the curve, the \(x\)-axis and the lines \(x = 1\) and \(x = 5\).
- Find the area of the shaded region.
The shaded region is rotated through four right angles about the \(x\)-axis.
- Find the volume of the solid formed, giving your answer in the form \(k \pi \ln 2\).