Use the definite integral ∫ 𝑓(𝑥) 𝑏 𝑎 𝑑𝑥 to determine the area under the curve 𝑦 = 𝑓(𝑥) between 𝑥 = 𝑎 and 𝑥 = 𝑏 if 𝑓(𝑥) > 0 over this interval.

A garden bed is modelled by the curve $f(x) = x(6 - x)$ where $f(x)$ is the height in metres and $x$ is the horizontal distance in metres. Use a definite integral to determine the area of the garden bed.

A region is bounded by the curve $y = 6 - x^2$, the $x$-axis, and the vertical lines $x = 1$ and $x = 2$. Which of the following represents the definite integral required to find the area of this region?

A rectangular storage tank is being drained. The rate at which water flows out of the tank is modelled by the function $r(t) = 12 - 0.5t$ litres per minute, where $t$ is the time in minutes after draining begins, for $0 \leq t \leq 20$. Use a definite integral to determine the total volume of water (in litres) that flows out of the tank during the 20-minute draining period.