Mathematics - Area Under Curves Question with Solution | TestHub

$y=\sqrt{x}$

$\sqrt{x}=x-2$

$(\sqrt{x}{)}^2-(\sqrt{x})-2=0$

$(\sqrt{x}-2)(\sqrt{x}+1)=0$

$\sqrt{x}=2\Rightarrow x=4$
Therefore, the area of the region is
${\int }_0^4\sqrt{x}dx- \mathrm{Area} \mathrm{of} ∆ABC$

$=\frac{2}{3}{x}^{3/2}{\overline{) }}_0^4-\frac{1}{2}\times 2\times 2$

$=\frac{2}{3}\times 4^{3/2}-2$
$=\frac{16}{3}-2=\frac{10}{3}\mathrm{sq}. \mathrm{unit}$