Easy -1.2 This is a straightforward application of the mean value formula for a function: (1/(b-a))∫[a to b]f(x)dx. With f(x)=x², the integral is elementary (x³/3), requiring only basic calculus recall and simple arithmetic. The multiple-choice format and 1-mark allocation confirm this is a routine, low-difficulty question, though the Further Maths context places it slightly above trivial.
The function f is defined by
$$f(x) = x^2 \quad (x \in \mathbb{R})$$
Find the mean value of \(f(x)\) between \(x = 0\) and \(x = 2\)
Circle your answer.
[1 mark]
\(\frac{2}{3}\) \(\frac{4}{3}\) \(\frac{8}{3}\) \(\frac{16}{3}\)
The function f is defined by
$$f(x) = x^2 \quad (x \in \mathbb{R})$$
Find the mean value of $f(x)$ between $x = 0$ and $x = 2$
Circle your answer.
[1 mark]
$\frac{2}{3}$ $\frac{4}{3}$ $\frac{8}{3}$ $\frac{16}{3}$
\hfill \mbox{\textit{AQA Further Paper 1 2024 Q3 [1]}}