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 curve \[y=\log x\,,\] \[x-\]axis and the ordinates \[x=1,\,\,x=2\] is                                               [MP PET 2004]

    A)            \[\log 4\]sq. unit                

    B)            \[(\log 4+1)\]sq. unit

    C)            \[(\log 4-1)\]sq. unit         

    D)            None of these

    Correct Answer: C

    Solution :

                       Given curve \[y=\log x\] and \[x=1\], \[x=2\].                    Hence required area = \[\int_{1}^{2}{\,\log \,x\,dx}\] = \[(x\,\log x-x)_{1}^{2}\]                                                                             = \[2\log 2-1=(\log 4-1)\]sq. unit.

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