Question

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

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

Answer 1

The correct option is C $\frac{10}{3}$


From the figure the area will be,
$A=\underset{0}{\overset{4}{\int }}\sqrt{x}dx-ar.\left(△ABC\right)\Rightarrow A=\frac{2}{3}{\left[x^{3/2}\right]}_0^4-\frac{1}{2}\times 2\times 2\Rightarrow A=\frac{10}{3}\text{sq. units.}$