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 parabola \[{{y}^{2}}=4ax,\] its axis and two ordinates \[x=4,\] \[x=9\] is

    A)            \[4{{a}^{2}}\]                       

    B)            \[4{{a}^{2}}.4\]

    C)            \[4{{a}^{2}}(9-4)\]             

    D)            \[\frac{152\sqrt{a}}{3}\]

    Correct Answer: D

    Solution :

                       Shaded area \[A=2\int_{4}^{9}{\sqrt{4ax}dx}\]            \[A=4\sqrt{a}\times \frac{2}{3}[{{x}^{3/2}}]_{4}^{9}=\frac{152\sqrt{a}}{3}\].

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