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

  • question_answer The area between the curve \[{{y}^{2}}=4ax,\] x-axis and the ordinates \[x=0\] and \[x=a\] is                                    [RPET 1996]

    A)            \[\frac{4}{3}{{a}^{2}}\]    

    B)            \[\frac{8}{3}{{a}^{2}}\]

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

    D)            \[\frac{5}{3}{{a}^{2}}\]

    Correct Answer: B

    Solution :

               Required area \[=2\int_{0}^{a}{\sqrt{4ax}dx}\]            \[=4\sqrt{a}\times \frac{2}{3}[{{x}^{3/2}}]_{0}^{a}=\frac{8\sqrt{a}}{3}.a\sqrt{a}=\frac{8}{3}{{a}^{2}}\].

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