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The diagram shows the curve \(y = \frac { 2 } { \sqrt { } x }\). The region \(R\), shaded in the diagram, is bounded by the curve and by the lines \(x = 1 , x = 5\) and \(y = 0\). The region \(R\) is rotated completely about the \(x\)-axis. Find the exact volume of the solid formed.
Use Simpson's rule, with 4 strips, to find an approximate value for
$$\int _ { 1 } ^ { 5 } \sqrt { } \left( x ^ { 2 } + 1 \right) \mathrm { d } x ,$$
giving your answer correct to 3 decimal places.