- In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
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\caption{Figure 2}
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Figure 2 shows a sketch of part of the curve with equation
$$y = \frac { 12 \sqrt { x } } { \left( 2 x ^ { 2 } + 3 \right) ^ { 1.5 } }$$
The region \(R\), shown shaded in Figure 2, is bounded by the curve, the line with equation \(x = \frac { 1 } { \sqrt { 2 } }\), the \(x\)-axis and the line with equation \(x = k\).
This region is rotated through \(360 ^ { \circ }\) about the \(x\)-axis to form a solid of revolution. Given that the volume of this solid is \(\frac { 713 } { 648 } \pi\), use algebraic integration to find the exact value of the constant \(k\).