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

  • question_answer
    \[\int_{-1}^{1}{{{\sin }^{11}}x\,dx}\] is equal to                                 [MNR 1995]

    A)                 \[\frac{10}{11}.\frac{8}{9}.\frac{6}{7}.\frac{4}{5}.\frac{2}{3}\]     

    B)                 \[\frac{10}{11}.\frac{8}{9}.\frac{6}{7}.\frac{4}{5}.\frac{2}{3}.\frac{\pi }{2}\]

    C)                 1             

    D)                 0

    Correct Answer: D

    Solution :

                    Since \[f(x)={{\sin }^{11}}x\]is an odd function, therefore \[\int_{-1}^{1}{{{\sin }^{11}}x\,\,dx}=0\].


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