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

  • question_answer
    \[\int_{-3}^{3}{\frac{{{x}^{2}}\sin 2x}{{{x}^{2}}+1}\,dx=}\]

    A)                 0             

    B)                 1

    C)                 \[2{{\log }_{e}}3\]           

    D)                 None of these

    Correct Answer: A

    Solution :

               Obviously the function \[\frac{{{x}^{2}}\sin 2x}{{{x}^{2}}+1}\]is odd, so                                 \[\int_{-3}^{3}{\frac{{{x}^{2}}\sin 2x}{{{x}^{2}}+1}\,}dx=0\].


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