6.
\includegraphics[max width=\textwidth, alt={}, center]{687756c0-2038-4077-8c5c-fe0ca0f6ce65-2_444_825_1571_516}
The diagram shows the curve with equation \(y = \sqrt { \frac { x } { x + 1 } }\).
The shaded region is bounded by the curve, the \(x\)-axis and the line \(x = 3\).
- Use Simpson's rule with six strips to estimate the area of the shaded region.
The shaded region is rotated through four right angles about the \(x\)-axis.
- Show that the volume of the solid formed is \(\pi ( 3 - \ln 4 )\).