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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 curve \[xy-3x-2y-10=0,\]x-axis and the lines \[x=3,x=4\]is                                                [AI CBSE 1991]

    A)            \[16\log 2-13\]                    

    B)            \[16\log 2-3\]                       

    C)            \[16\log 2+3\]                      

    D)            None of these

    Correct Answer: C

    Solution :

                       Given curve is \[y(x-2)=3x+10\Rightarrow y=\frac{3x+10}{x-2}\]            Required area is \[\int_{3}^{4}{\,\,y\,dx=\int_{3}^{4}{\frac{3x+10}{x-2}\,\,dx}}\]                    =\[[3x+16\log (x-2)]_{3}^{4}=3+16\log 2\] sq. unit.


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