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JEE Main & Advanced Mathematics Definite Integration Question Bank Properties of Definite Integration

  • question_answer
    The value of \[\int_{-1}^{1}{(\sqrt{1+x+{{x}^{2}}}-\sqrt{1-x+{{x}^{2}}})\,dx}\] is

    A)                 0             

    B)                 1

    C)                 \[-1\]    

    D)                 None of these

    Correct Answer: A

    Solution :

               Let \[f(x)=\sqrt{1+x+{{x}^{2}}}-\sqrt{1-x+{{x}^{2}}}\].                    Then \[f(-x)=\sqrt{1-x+{{x}^{2}}}-\sqrt{1+x+{{x}^{2}}}=-f(x)\]                                 Hence \[f(x)\] is an odd function and so \[\int_{-1}^{1}{f(x)dx=0}\].


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