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JEE Main & Advanced Mathematics Definite Integration Question Bank Fundamental definite integration, Definite integration by substitution

  • question_answer
    The value of \[\int_{1}^{2}{\log x\,dx}\] is                                            [Roorkee 1995]

    A)                 \[\log 2/e\]        

    B)                 \[\log 4\]

    C)                 \[\log 4/e\]        

    D)                 \[\log 2\]

    Correct Answer: C

    Solution :

               \[\int_{1}^{2}{\log xdx=[x\log x-x]_{1}^{2}=2\log 2-2+1}\]                                                  \[=\log 4-1=\log 4-\log e=\log \frac{4}{e}\].


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