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

  • question_answer The area bounded by the curves \[{{y}^{2}}-x=0\] and \[y-{{x}^{2}}=0\] is                                            [MP PET 1997]

    A)            \[\frac{7}{3}\]                      

    B)            \[\frac{1}{3}\]

    C)            \[\frac{5}{3}\]                      

    D)            1

    Correct Answer: B

    Solution :

               \[\int_{0}^{1}{(\sqrt{x}-{{x}^{2}})dx=\left( \frac{{{x}^{3/2}}}{3/2}-\frac{{{x}^{3}}}{3} \right)_{0}^{1}=\frac{1}{3}}\].

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