10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d31369fa-9532-4a09-b67d-a3a3cbf7d586-30_639_878_246_596}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
Figure 2 shows a sketch of part of the curve \(C\) with equation
$$y = \frac { 1 } { 3 } x ^ { 2 } - 2 \sqrt { x } + 3 \quad x \geqslant 0$$
The point \(P\) lies on \(C\) and has \(x\) coordinate 4
The line \(l\) is the tangent to \(C\) at \(P\).
- Show that \(l\) has equation
$$13 x - 6 y - 26 = 0$$
The region \(R\), shown shaded in Figure 2, is bounded by the \(y\)-axis, the curve \(C\), the line \(l\) and the \(x\)-axis.
- Find the exact area of \(R\).