Question

$A$: The area bounded by $x=3,y^2=3x$
$B$: The area bounded by $y=1-|x|$ and X-axis
$C$: The area enclosed between the curve $y=x^2$ and the line $y=\sqrt{3}x$
The descending order of $A,B,C$ is

• A. $A,C,B$
• B. $C,B,A$
• C. $A,B,C$
• D. $C,A,B$

Answer 1

Answer: (C)

$A,B,C$

A:

$2{\int }_0^3\sqrt{3x}dx$

$\Rightarrow \frac{4\sqrt{3}}{3}{\left|x^{\frac{3}{2}}\right|}_0^3$

$=\frac{4\sqrt{3}}{3}\times \sqrt{3}\times 3$

$=12squnits.$

B:

$\frac{1}{2}\times 2\times 1=1squnits.$

C:

$\stackrel{\sqrt{3}}{\underset{0}{\int }}(\sqrt{3}x-x^2)dx=\frac{\sqrt{3}{x}^2}{2}-\frac{x^3}{3}{|}_0^{\sqrt{3}}$

$=\frac{3\sqrt{3}}{2}-\frac{3\sqrt{3}}{3}$

$=\frac{\sqrt{3}}{2}sq.units$

So, descending order
A > B > C.