- The curve \(C\) has parametric equations
$$x = \ln t , \quad y = t ^ { 2 } - 2 , \quad t > 0$$
Find
- an equation of the normal to \(C\) at the point where \(t = 3\),
- a cartesian equation of \(C\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a3ece8a8-8107-4c3a-a6a9-c19b5e35ec5a-10_579_759_740_571}
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\caption{Figure 1}
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The finite area \(R\), shown in Figure 1, is bounded by \(C\), the \(x\)-axis, the line \(x = \ln 2\) and the line \(x = \ln 4\). The area \(R\) is rotated through \(360 ^ { \circ }\) about the \(x\)-axis. - Use calculus to find the exact volume of the solid generated.