Question

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

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

Answer 1

Answer: (B)

$y=-\sqrt{-x}\Rightarrow y^2=-x$ where $x\&y$ both $(-)$ ve
$x=-\sqrt{-y}\Rightarrow x^2=-y$ where $x\&y$ both $(-)$ ve
Hence $A=\frac{16ab}{3}$
where $a=b=\frac{1}{4}$
$\therefore A=\frac{1}{3}\Rightarrow (B)$