JAMB 1999 · UME · Q36✱✱

Find the area bounded by the curve $y = x(2 - x)$ , the $x$ -axis, $x = 0$ and $x = 2$ .

Worked solution (try it first)

Expand: $y = 2x - x^2$ .
It is above the $x$ -axis between $x = 0$ and $x = 2$ , so the area is $\int_0^2 (2x - x^2)\,dx$ .
Integrate term by term: $x^2 - \frac{x^3}{3}$ .
At $x = 2$ this is $4 - \frac83 = \frac43$ , and at $x = 0$ it is 0.
So the area is $1\frac13$ square units, option C.