6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a4ac7e65-267e-45c0-bbf2-2c38608eacc3-10_581_823_146_477}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the curve with equation \(y = x \sqrt { 1 - x } , 0 \leq x \leq 1\).
- Use the substitution \(u ^ { 2 } = 1 - x\) to show that the area of the region bounded by the curve and the \(x\)-axis is \(\frac { 4 } { 15 }\).
- Find, in terms of \(\pi\), the volume of the solid formed when the region bounded by the curve and the \(x\)-axis is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.
6. continued