NationalHardCalculus10–12

Area Between a Parabola and the Axis

Área Entre uma Parábola e o Eixo

The curve $y = 6x - x^{2}$ meets the $x$ -axis at two points. Find those points and the area of the region enclosed between the curve and the axis.

The limits of integration are not given: they are the zeros of the function. Check the sign of $y$ between them before deciding whether the integral already is the area.

Solution

Step 1 of 4

1.Zeros: $6x - x^{2} = x(6 - x) = 0$ , so $x = 0$ and $x = 6$ .