The equation sin⁡x+xcos⁡x=0   has at least one root in the interval 

The equation sinx+xcosx=0   has at least one root in the interval 

  1. A

    (π/2,0)

  2. B

    (0,π)

  3. C

    (π/2,π/2)

  4. D

    none of these  

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    Solution:

     Consider the function f(x)  given by 

    f(x)=(sinx+xcosx)dx=xsinx

    We observe that  

    f(0)=f(π)=0 

    Therefore, 0 and π are two roots of f(x)=0 

    Consequently f(x)=0 i.e. sinx+xcosx=0  has at least one 

    root in  (0,π) 

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