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

  • question_answer
    \[\int_{-1}^{1}{{{x}^{17}}{{\cos }^{4}}x}\,dx=\]                                      [MP PET 1990]

    A)                 \[-2\]    

    B)                 \[-1\]

    C)                 0             

    D)                 2

    Correct Answer: C

    Solution :

               Let \[f(x)={{x}^{17}}{{\cos }^{4}}x\]                          \[f(-x)={{(-x)}^{17}}{{\left\{ \cos (-x) \right\}}^{4}}=-f(x)\]                                 Therefore,\[\int_{-1}^{1}{{{x}^{17}}{{\cos }^{4}}x\,dx=0}\].


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