Question

The area (in sq. units) of the region $\{xϵR:x\ge 0,y\ge 0,y\ge x-2andy\le \sqrt{x}\}$, is

• A. $\frac{13}{3}$
• B. $\frac{10}{3}$
• C. $\frac{5}{3}$
• D. $\frac{8}{3}$

Answer 1

Answer: (B)

$\frac{10}{3}$

Here, $y\ge x-2$ and $y\le \sqrt{x}$

The line $y=x-2$ intersects $y=\sqrt{x}$ at $(4,2)$.

The area enclosed by the required curve is

${\int }_0^4\sqrt{x}dx-\frac{1}{2}\times 2\times 2=\frac{16}{3}-2=\frac{10}{3}$

So, option B is the correct answer.