The first set of axes below shows the graph of \(y = {\text{ }}f(x)\) for \( - 4 \leqslant x \leqslant 4\).

Let \(g(x) = \int_{ - 4}^x {f(t){\text{d}}t} \) for \( - 4 \leqslant x \leqslant 4\).

(a)     State the value of x at which \(g(x)\) is a minimum.

(b)     On the second set of axes, sketch the graph of \(y = g(x)\).

(a)     \(x = 1\)     A1

[1 mark]

(b)     A1 for point (–4, 0)

A1 for (0, − 4)

A1 for min at \(x = 1\) in approximately the correct place

A1 for (4, 0)

A1 for shape including continuity at \(x = 0\)

[5 marks]

Total [6 marks]