Question

The correct statement(s) among the following about area between two curves is\are

• A. The area bounded by the curves $y=-\sqrt{-x}$ and $x=-\sqrt{-y},x,y\le 0$ is $1$ sq. units
• B. The area bounded by the curves $y=-\sqrt{-x}$ and $x=-\sqrt{-y},x,y\le 0$ is $\frac{3}{4}$ sq. units
• C. The area bounded by the curves $y=x^2$ and $y=\sqrt{|x|},$ is $\frac{3}{4}$ sq. units
• D. The area bounded by the curves $y=x^2$ and $y=\sqrt{|x|},$ is $\frac{2}{3}$ sq. units

Answer 1

The correct option is D The area bounded by the curves $y=x^2$ and $y=\sqrt{|x|},$ is $\frac{2}{3}$ sq. units

Curve$:1$


Required area $=\underset{-1}{\overset{0}{\int }}|-\sqrt{-x}+x^2|dx=\frac{1}{3}$

Curve$:2$


Required area
$=2\underset{0}{\overset{1}{\int }}(\sqrt{x}-x^2)dx=\frac{2}{3}$