Question

Find the area bounded by the curve 𝑦 = (𝑥^2)/4

and 𝑥 + 4 = 2y

Answer 1

$$y=\dfrac{x^2}{4}$$

$$x+4=2y=>y=\dfrac{1}{2}x+2$$

$$\dfrac{x^2}{4}=\dfrac{1}{2}x+2$$

$$x^2-2x-8=0$$

$$(x+2)(x-4)=0$$

$$x_1=-2, x_2=4$$

$$A=\displaystyle\int_{-2}^{4}(\dfrac{1}{2}x+2-\dfrac{x^2}{4})dx=$$

$$=\big[\dfrac{x^2}{4}+2x-\dfrac{x^3}{12}\big]\begin{matrix} 4 \\ -2 \end{matrix}$$

$$=4+8-\dfrac{16}{3}-(1-4+\dfrac{2}{3})=9(units^2)$$

$A=9$ square units