GATE EC 2025 Set 1 Q41 — Calculus

Consider a non-negative function $f(x)$ which is continuous and bounded over the interval $[2,8]$. Let $M$ and $m$ denote, respectively, the maximum and the minimum values of $f(x)$ over the interval.

Among the combinations of $\alpha$ and $\beta$ given below, choose the one(s) for which the inequality
$$\beta \leq \int_{2}^{8} f(x) d x \leq \alpha$$

is guaranteed to hold.