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 bounded by the curve \[9{{x}^{2}}+4{{y}^{2}}-36=0\] is                                   [Karnataka CET 2005]

    A)            \[9\pi \]                                  

    B)            \[4\pi \]

    C)            \[36\pi \]                               

    D)            \[6\pi \]                                  

    Correct Answer: D

    Solution :

               \[9{{x}^{2}}+4{{y}^{2}}=36\] Þ \[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{9}=1\], which is equation of an ellipse. Remember area enclosed by ellipse is \[\pi \,ab\]i.e., \[\pi \ 2.3=6\pi \].

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