JEE Main & Advanced Sample Paper JEE Main - Mock Test - 6

  • question_answer
    The area of the region bounded by the curves \[y={{x}^{3}},y=\frac{1}{x},x=2\] is

    A) \[4-{{\log }_{e}}2\]

    B) \[\frac{1}{4}+{{\log }_{e}}2\]

    C) \[3-{{\log }_{e}}2\]       

    D) \[\frac{15}{4}-{{\log }_{e}}2\]

    Correct Answer: D

    Solution :

    [d]: The point of intersection of the curves\[y={{x}^{3}}\]and\[y=1/x\]is (1,1) \[\therefore \]The required area \[=\int\limits_{1}^{2}{\left( {{x}^{3}}-\frac{1}{x} \right)dx}\] \[=\left[ \frac{{{x}^{4}}}{4}-\log x \right]_{1}^{2}=4-{{\log }_{e}}2-\frac{1}{4}\] \[=\left( \frac{15}{4}-{{\log }_{e}}2 \right)\text{sq}\text{.}\,\text{units}\]

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