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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-7

  • question_answer
    The value of integral\[\int\limits_{-1}^{1}{{{\sin }^{15}}x.dx}\]is:

    A)  1                                  

    B)  0

    C)  \[\frac{14}{15}\times \frac{12}{13}\times \frac{10}{11}\times \frac{8}{9}\times \frac{6}{7}\times \frac{4}{5}\times \frac{2}{3}\]              

    D)   None of these

    Correct Answer: B

    Solution :

    [b] \[\because I=\int\limits_{-1}^{1}{si{{n}^{15}}x.dx}\] \[\because of(x)=si{{n}^{15}}x\] \[\therefore f(-x)={{\{sinn(-x)\}}^{15}}=-si{{n}^{15}}x\] \[\because f(x)\]is odd function, so by the property of definite integral             \[I=\int\limits_{-1}^{1}{f(x)=dx}=0\]             \[I=\int\limits_{-1}^{1}{{{\sin }^{15}}x=dx}=0\]


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