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

  • question_answer Area bounded by parabola \[{{y}^{2}}=x\] and straight line \[2y=x\] is                                                    [MP PET 1996]

    A)            \[\frac{4}{3}\]                      

    B)            1

    C)            \[\frac{2}{3}\]                      

    D)            \[\frac{1}{3}\]

    Correct Answer: A

    Solution :

                       \[{{y}^{2}}=x\]and \[2y=x\Rightarrow {{y}^{2}}=2y\Rightarrow y=0,\,2\]                     \[\therefore \,\]Required area\[=\int_{0}^{2}{({{y}^{2}}-2y)dy=\left( \frac{{{y}^{3}}}{3}-{{y}^{2}} \right)_{0}^{2}=\frac{4}{3}}\]sq. unit.


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