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

  • question_answer
    \[\int_{1}^{\sqrt{3}}{\frac{1}{1+{{x}^{2}}}dx}\] is equal to                                            [DCE 2002]

    A)                 \[\pi /12\]          

    B)                 \[\pi /6\]

    C)                 \[\pi /4\]             

    D)                 \[\pi /3\]

    Correct Answer: A

    Solution :

                    \[\int_{1}^{\sqrt{3}}{\frac{1}{1+{{x}^{2}}}dx=[{{\tan }^{-1}}x]_{\,1}^{\sqrt{3}}=\frac{\pi }{3}-\frac{\pi }{4}=\frac{\pi }{12}}\].


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