11.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2ce10759-9ce6-47a1-b55d-d22082f88f55-28_668_743_251_662}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
Figure 5 shows a sketch of part of the curve \(C\) with equation
$$y = 8 x ^ { 2 } \mathrm { e } ^ { - 3 x } \quad x \geqslant 0$$
The finite region \(R\), shown shaded in Figure 5, is bounded by
- the curve \(C\)
- the line with equation \(x = 1\)
- the \(x\)-axis
Find the exact area of \(R\), giving your answer in the form
$$A + B \mathrm { e } ^ { - 3 }$$
where \(A\) and \(B\) are rational numbers to be found.