question_answer

The area enclosed by the parabolas \[y={{x}^{2}}-1\] and \[y=1-{{x}^{2}}\] is                                      [AMU 1999]

A)            1/3

B)            2/3

C)            4/3

D)            8/3

Correct Answer: D

Solution :

           Given parabolas are \[{{x}^{2}}=1+y\],  \[{{x}^{2}}=1-y\]            Required area \[=4\int_{0}^{1}{(1-{{x}^{2}})\,dx}\]\[=4\left[ x-\frac{{{x}^{3}}}{3} \right]_{0}^{1}=\frac{8}{3}\].