• question_answer Area of the region enclosed between the curves $x={{y}^{2}}-1$ and $x=\,\,|y|\sqrt{1-{{y}^{2}}}$ is A) 1 B) 4/3 C) 2/3 D) 2

 $\because$       $x={{y}^{2}}-1,$       $x=\,\,|y|\sqrt{1-{{y}^{2}}}$ $\therefore$ $=2\,\,\left[ \int\limits_{0}^{1}{y\sqrt{1-{{y}^{2}}}}dy+\left| \int\limits_{0}^{1}{({{y}^{2}}-1})\,dy \right| \right]$$=2\,\,\left[ \frac{1}{3}+\left| -\frac{2}{3} \right| \right]=2\,\,\left[ \frac{1}{3}+\frac{2}{3} \right]=2$