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

  • question_answer Area enclosed by the parabola \[ay=3({{a}^{2}}-{{x}^{2}})\] and x-axis is

    A)            \[4\,{{a}^{2}}\]sq. unit     

    B)            \[12\,{{a}^{2}}\]sq. unit

    C)            \[4\,{{a}^{3}}\]sq. unit     

    D)            None of these

    Correct Answer: A

    Solution :

               The parabola meets x-axis at the points, where \[\frac{3}{a}({{a}^{2}}-{{x}^{2}})=0\Rightarrow x=\pm a.\] So the required area                    \[=\int_{-a}^{a}{\frac{3}{a}({{a}^{2}}-{{x}^{2}})dx=\frac{6}{a}\int_{0}^{a}{\,({{a}^{2}}-{{x}^{2}})dx=4{{a}^{2}}}}\]sq. unit.

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