5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e877dc80-4cfc-4c8b-9640-9b186cd7ab13-08_617_917_146_475}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the curve with equation \(y = 4 x ^ { \frac { 1 } { 2 } } \mathrm { e } ^ { - x }\).
The shaded region is bounded by the curve, the \(x\)-axis and the line \(x = 2\).
- Use the trapezium rule with four intervals of equal width to estimate the area of the shaded region.
The shaded region is rotated through \(2 \pi\) radians about the \(x\)-axis.
- Find, in terms of \(\pi\) and e, the exact volume of the solid formed.
5. continued