Let $$A_{1}$$ be the bounded area enclosed by the curves $$y=x^{2}+2,x+Y=8$$ and y-axis that lies in the first quadrant. Let $$A_{2}$$ be the bounded area enclosed by the curves $$y=x^{2}+2,y^{2}=x,x=2$$ and y-axis that lies in the first quadrant. Then $$A_{1}-A_{2}$$ is equal to

A

$$\frac{2}{3}(2\sqrt{2}+1)$$

B

$$\frac{2}{3}(\sqrt{2}+1)$$

C

$$\frac{2}{3}(4\sqrt{2}+1)$$

D

$$\frac{2}{3}(3\sqrt{2}+1)$$