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The diagram shows the curve with equation \(y = \frac { 1 } { \sqrt { 3 x + 2 } }\). The shaded region is bounded by the curve and the lines \(x = 0 , x = 2\) and \(y = 0\).
- Find the exact area of the shaded region.
- The shaded region is rotated completely about the \(x\)-axis. Find the exact volume of the solid formed, simplifying your answer.