Standard +0.3 This is a straightforward area calculation requiring finding intersection points (solving a simple quadratic), then computing a definite integral of a polynomial. The setup is clear, the algebra is routine (expanding (x-4)² and integrating), and it's a standard textbook exercise with no conceptual challenges beyond basic integration technique.
\includegraphics{figure_14}
The diagram above shows the curve with equation
$$y = (x-4)^2, \quad x \in \mathbb{R},$$
intersected by the straight line with equation \(y = 4\), at the points \(A\) and \(B\).
The curve meets the \(y\) axis at the point \(C\).
Calculate the exact area of the shaded region, bounded by the curve and the straight line segments \(AB\) and \(BC\). [8]
\includegraphics{figure_14}
The diagram above shows the curve with equation
$$y = (x-4)^2, \quad x \in \mathbb{R},$$
intersected by the straight line with equation $y = 4$, at the points $A$ and $B$.
The curve meets the $y$ axis at the point $C$.
Calculate the exact area of the shaded region, bounded by the curve and the straight line segments $AB$ and $BC$. [8]
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q14 [8]}}