Easy -1.2 This is a straightforward application of understanding signed area in definite integrals. Students only need to recognize that region A (below x-axis) contributes -189 and region B (above x-axis) contributes +64, giving -189 + 64 = -125. It's a single-step conceptual question worth 1 mark with multiple choice format, requiring only basic understanding of how integrals relate to signed area rather than any calculation.
The graph of \(y = f(x)\) intersects the \(x\)-axis at \((-3, 0)\), \((0, 0)\) and \((2, 0)\) as shown in the diagram below.
\includegraphics{figure_2}
The shaded region \(A\) has an area of 189
The shaded region \(B\) has an area of 64
Find the value of \(\int_{-3}^{2} f(x) \, dx\)
Circle your answer.
[1 mark]
\(-253\) \(\quad\) \(-125\) \(\quad\) \(125\) \(\quad\) \(253\)
The graph of $y = f(x)$ intersects the $x$-axis at $(-3, 0)$, $(0, 0)$ and $(2, 0)$ as shown in the diagram below.
\includegraphics{figure_2}
The shaded region $A$ has an area of 189
The shaded region $B$ has an area of 64
Find the value of $\int_{-3}^{2} f(x) \, dx$
Circle your answer.
[1 mark]
$-253$ $\quad$ $-125$ $\quad$ $125$ $\quad$ $253$
\hfill \mbox{\textit{AQA Paper 2 2024 Q2 [1]}}