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 the parabola \[{{y}^{2}}=4ax\] and its latus rectum is                                  [RPET 1997, 2000, 02]

    A)            \[\frac{2}{3}{{a}^{2}}\]sq. unit                                         

    B)            \[\frac{4}{3}{{a}^{2}}\]sq. unit

    C)            \[\frac{8}{3}{{a}^{2}}\]sq. unit                                         

    D)            \[\frac{3}{8}{{a}^{2}}\]sq. unit

    Correct Answer: C

    Solution :

               Area = \[2\int_{0}^{a}{\,\,y\,dx=2\int_{0}^{a}{\sqrt{4ax}}\,\,dx}\]            \[2\times 2\sqrt{a}\times \frac{2}{3}\left| {{x}^{3/2}} \right|_{0}^{a}=\frac{8}{3}{{a}^{2}}\] sq. unit.

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