8. The function \(f\) is defined by
$$f ( x ) = \frac { 1 } { \sqrt { x ^ { 2 } + 4 x + 3 } }$$
- Find the mean value of the function \(f\) for \(0 \leqslant x \leqslant 2\), giving your answer correct to three decimal places.
- The region \(R\) is bounded by the curve \(y = f ( x )\), the \(x\)-axis and the lines \(x = 0\) and \(x = 2\). Find the exact value of the volume of the solid generated when \(R\) is rotated through four right angles about the \(x\)-axis.