Question

The area (in sq. units) of the region $\{(x,y):x\ge 0,x+y\le 3,x^2\le 4y$ and $y\le 1+\sqrt{x}\}$ is

• A. $\frac{3}{2}$
• B. $\frac{7}{3}$
• C. $\frac{5}{2}$
• D. $\frac{59}{12}$

Answer 1

Answer: (C)

Area of shaded region
$=\underset{0}{\overset{1}{\int }}$$\left(\sqrt{x}+1-\frac{x^2}{4}\right)dx+$$=\underset{1}{\overset{2}{\int }}$$\left(\left(3-x\right)-\frac{x^2}{4}\right)dx$
$=\frac{5}{2}$ sq. unit