Question

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

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

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 $A =\frac{16 ab }{3}$
where $a=b=\frac{1}{4}$
$\therefore A =\frac{1}{3} \Rightarrow( B )$