Question

The area (in sq. units) bounded by the curve $y=\sqrt{x},2y-x+3=0,x$-axis, and lying in first quadrant is :

• A. $9$
• B. $36$
• C. $18$
• D. $\frac{27}{4}$

Answer 1

The correct option is A $9$

$2y-x+3=\mathrm{0...}\left(1\right)$
$y=\sqrt{x}\Rightarrow y^2=x$ put in equation $\left(1\right)$
$\Rightarrow 2y-y^2+3=0$
$\Rightarrow (y+1)(y-3)=0$
$\Rightarrow y=-1,y=3$
$\therefore x=y^2=9$
Let's draw the graph

Area of shaded region $=\underset{0}{\overset{9}{\int }}\sqrt{x}dx-\text{area of}△ABC$
$=\frac{2}{3}{\left[x^{3/2}\right]}_0^9-\frac{1}{2}\times 3\times 6$
$=9$ sq. units