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

  • question_answer
    \[\int_{\,-\,1}^{\,0}{\frac{dx}{{{x}^{2}}+2x+2}=}\]                                 [MP PET 2000]

    A)                 0             

    B)                 \[\pi /4\]

    C)                 \[\pi /2\]             

    D)                 \[-\pi /4\]

    Correct Answer: B

    Solution :

               \[I=\int_{-1}^{0}{\frac{dx}{{{x}^{2}}+2x+2}}\]\[=\int_{-1}^{0}{\frac{dx}{{{(x+1)}^{2}}+1}}\]                                   \[=[{{\tan }^{-1}}(x+1)]_{-1}^{0}\]\[=[{{\tan }^{-1}}1-{{\tan }^{-1}}0]=\frac{\pi }{4}\].


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