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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 \[y=4{{x}^{2}},\] \[y-\]axis and the lines \[y=1,\,\,y=4\] is              [MNR 1990]

    A)            3 sq. unit                                

    B)            \[\frac{7}{5}\]sq. unit

    C)            \[\frac{7}{3}\]sq. unit       

    D)            None of these

    Correct Answer: C

    Solution :

                       Required area = \[\int_{1}^{4}{x\,dy=\int_{1}^{4}{\frac{\sqrt{y}}{2}dy}}\]                                                                          = \[\frac{1}{2}.\frac{2}{3}|{{y}^{3/2}}|_{1}^{4}=\frac{7}{3}\] sq. unit.


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