Easy -1.8 This is a 1-mark multiple choice question requiring only recognition that area between curves is ∫(upper - lower)dx. Students need to identify the limits (x = 0 to 5 from intersection points) and simplify (7-2x)-(x²-7x+7) = 5x-x², then select the matching option. No calculation required, just pattern matching.
The shaded region, shown in the diagram below, is defined by
$$x^2 - 7x + 7 \leq y \leq 7 - 2x$$
\includegraphics{figure_2}
Identify which of the following gives the area of the shaded region.
Tick (\(\checkmark\)) one box.
[1 mark]
\(\int (7 - 2x) \, dx - \int (x^2 - 7x + 7) \, dx\)
\(\int_0^5 (x^2 - 5x) \, dx\)
\(\int_0^5 (5x - x^2) \, dx\)
\(\int_0^5 (x^2 - 9x + 14) \, dx\)
The shaded region, shown in the diagram below, is defined by
$$x^2 - 7x + 7 \leq y \leq 7 - 2x$$
\includegraphics{figure_2}
Identify which of the following gives the area of the shaded region.
Tick ($\checkmark$) one box.
[1 mark]
$\int (7 - 2x) \, dx - \int (x^2 - 7x + 7) \, dx$
$\int_0^5 (x^2 - 5x) \, dx$
$\int_0^5 (5x - x^2) \, dx$
$\int_0^5 (x^2 - 9x + 14) \, dx$
\hfill \mbox{\textit{AQA Paper 3 2022 Q2 [1]}}