question_answer

Area of the region enclosed between the Curves \[x={{y}^{2}}-1\] and \[x=\left| \,y\, \right|\sqrt{1-{{y}^{2}}}\] is -

A) 1

B) 4/3  

C) 2/3

D) 2

Correct Answer: D

Solution :

\[\because x={{y}^{2}}-1,\] \[x=\left| \,y\, \right|\sqrt{1-{{y}^{2}}}\]

\[\therefore \] Required area

\[=2\,\,\left[ \int\limits_{0}^{1}{y\sqrt{1-{{y}^{2}}}dy+\left| \int\limits_{0}^{1}{({{y}^{2}}-1)dy} \right|} \right]\]

\[=2\,\,\left[ \frac{1}{3}+\left| -\,\frac{2}{3} \right| \right]=2\,\,\left[ \frac{1}{3}+\frac{2}{3} \right]=2\]