\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a5579938-e202-4543-8513-6483ede49850-03_410_552_205_694}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows part of the curve \(y = \frac { 3 } { \sqrt { } ( 1 + 4 x ) }\). The region \(R\) is bounded by the curve, the \(x\)-axis, and the lines \(x = 0\) and \(x = 2\), as shown shaded in Figure 1.
- Use integration to find the area of \(R\).
The region \(R\) is rotated \(360 ^ { \circ }\) about the \(x\)-axis.
- Use integration to find the exact value of the volume of the solid formed.