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 curve \[{{y}^{2}}=x,\] line \[y=4\] and y-axis is                          [Roorkee 1995; RPET 2003]

    A)            \[\frac{16}{3}\]                   

    B)            \[\frac{64}{3}\]

    C)            \[7\sqrt{2}\]                         

    D)            None of these

    Correct Answer: B

    Solution :

                       Required area = area of OABC ? area of OBC                                       \[=16\times 4-\int_{0}^{16}{\sqrt{x}}dx=64-\left[ \frac{{{x}^{3/2}}}{3/2} \right]_{0}^{16}=\frac{64}{3}.\]

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