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

  • question_answer The area of the region (in the square unit) bounded by the curve \[{{x}^{2}}=4y,\] line \[x=2\] and x-axis is         [MP PET 2002]

    A)            1    

    B)            \[\frac{2}{3}\]

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

    D)            \[\frac{8}{3}\]

    Correct Answer: B

    Solution :

                       Given \[{{x}^{2}}=4y\]                    Shaded area \[=\int_{0}^{2}{\frac{{{x}^{2}}}{4}dx}\]\[=\frac{1}{12}[{{x}^{3}}]_{0}^{2}=\frac{8}{12}=\frac{2}{3}\].

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