Determine the area $\mathscr{A}$, expressed in square units, of the shaded region in the graph of Part A (the region bounded by the curve $\mathscr{C}_u$ where $u(x) = \frac{x^2 - 5x + 4}{x^2}$ between its zeros $x=1$ and $x=4$).
For all real $\lambda$ greater than or equal to 4, we denote by $\mathscr{A}_{\lambda}$ the area, expressed in square units, of the region formed by the points $M$ with coordinates $(x; y)$ such that $$4 \leqslant x \leqslant \lambda \quad \text{and} \quad 0 \leqslant y \leqslant u(x).$$ Does there exist a value of $\lambda$ for which $\mathscr{A}_{\lambda} = \mathscr{A}$?
\begin{enumerate}
\item Determine the area $\mathscr{A}$, expressed in square units, of the shaded region in the graph of Part A (the region bounded by the curve $\mathscr{C}_u$ where $u(x) = \frac{x^2 - 5x + 4}{x^2}$ between its zeros $x=1$ and $x=4$).
\item For all real $\lambda$ greater than or equal to 4, we denote by $\mathscr{A}_{\lambda}$ the area, expressed in square units, of the region formed by the points $M$ with coordinates $(x; y)$ such that
$$4 \leqslant x \leqslant \lambda \quad \text{and} \quad 0 \leqslant y \leqslant u(x).$$
Does there exist a value of $\lambda$ for which $\mathscr{A}_{\lambda} = \mathscr{A}$?
\end{enumerate}