Question

The area bounded by the curves $y=-\sqrt{-x}$ and $x=-\sqrt{-y}$ were $x,y\le 0$

• A. Can not be determined
• B. is 1/3
• C. is 2/3
• D. is same as that of the figure by the curves $y=\sqrt{-x};x\le 0$ and $x=\sqrt{-y};y\le 0$

Answer 1

Answer: (B), (D)

The correct options are
B is 1/3
D is same as that of the figure by the curves $y=\sqrt{-x};x\le 0$ and $x=\sqrt{-y};y\le 0$

$y_1=-\sqrt{-x}$
$y_2=-x^2$
Area bound is given by,

$={\int }_{-1}^0(y_1+y_2)dx$

$={\int }_{-1}^0(-\sqrt{-x}+x^2)dx$

$={[\frac{-x^{3/2}}{3/2}+\frac{x^3}{3}]}_{-1}^0$

$=(0-0)-(\frac{-2}{3}+\frac{1}{3})$

$=\frac{1}{3}$