question_answer

The area enclosed by the parabolas \[\operatorname{y}={{x}^{2}}-1\]and \[y=1-{{x}^{2}}\] is

A) 1/3                              

B) 2/3

C) 4/3                              

D) 8/3

Correct Answer: D

Solution :

Given parabolas are \[{{\operatorname{x}}^{2}}=1 +y, {{x}^{2}}= 1 -y\] \[\therefore \,\,\,required\,\,area=\,\,4\int\limits_{0}^{1}{(1-{{x}^{2}})dx}=4\left[ x-\frac{{{x}^{3}}}{3} \right]_{0}^{1}=\frac{8}{3}\]