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

  • question_answer
    The value of \[\int_{3}^{5}{\frac{{{x}^{2}}}{{{x}^{2}}-4}\,dx}\] is                                                [Roorkee 1992]

    A)                 \[2-{{\log }_{e}}\left( \frac{15}{7} \right)\]

    B)                 \[2+{{\log }_{e}}\left( \frac{15}{7} \right)\]

    C)                 \[2+4{{\log }_{e}}3-4{{\log }_{e}}7+4{{\log }_{e}}5\]

    D)                 \[2-{{\tan }^{-1}}\left( \frac{15}{7} \right)\]

    Correct Answer: B

    Solution :

                    \[I=\int_{3}^{5}{\left( 1+\frac{4}{{{x}^{2}}-4} \right)}\,dx.\]Now proceed yourself.


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