JEE Main & Advanced Mathematics Definite Integration Question Bank Area Bounded by Region, Volume and Surface Area of Solids of Revolution

  • 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 \[=4\int_{0}^{1}{(1-{{x}^{2}})\,dx}\]\[=4\left[ x-\frac{{{x}^{3}}}{3} \right]_{0}^{1}=\frac{8}{3}\].


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