7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4232f6a1-00ff-4e88-b5f4-1abf3d4742c4-12_560_911_146_456}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the curve with parametric equations
$$x = t ^ { 3 } + 1 , \quad y = \frac { 2 } { t } , \quad t > 0 .$$
The shaded region is bounded by the curve, the \(x\)-axis and the lines \(x = 2\) and \(x = 9\).
- Find the area of the shaded region.
- Show that the volume of the solid formed when the shaded region is rotated through \(2 \pi\) radians about the \(x\)-axis is \(12 \pi\).
- Find a cartesian equation for the curve in the form \(y = \mathrm { f } ( x )\).
7. continued