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\includegraphics[max width=\textwidth, alt={}, center]{b6b6e55a-a5ba-466c-ac9f-b5ef5bca7a3c-2_419_707_1576_660}
The diagram shows the curve
$$y = \frac { 1 } { \sqrt { } ( 4 x + 1 ) }$$
The region \(R\) (shaded in the diagram) is enclosed by the curve, the axes and the line \(x = 2\).
- Show that the exact area of \(R\) is 1 .
- The region \(R\) is rotated completely about the \(x\)-axis. Find the exact volume of the solid formed.