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

  • question_answer If the area above the x-axis, bounded by the curves \[y={{2}^{kx}}\] and \[x=0\] and \[x=2\] is \[\frac{3}{\ln 2},\] then the value of k is                                                                       [Orissa JEE 2003]

    A)            \[\frac{1}{2}\]                      

    B)            1

    C)            \[-1\]                                       

    D)            2

    Correct Answer: B

    Solution :

               \[\int_{\,0}^{\,2}{{{2}^{kx}}dx=\frac{3}{\log 2}\Rightarrow {{2}^{2k}}-1=3k}\]. Now check from options, only  satisfies the above condition.

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