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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 32

  • question_answer
    \[\int\limits_{0}^{\pi /4}{sinxd\left( x-\left[ x \right] \right)}\] is equal to, where [x] denotes greatest integer function -

    A) \[\frac{1}{2}\]  

    B)                    \[1-\frac{1}{\sqrt{2}}\]

    C) 1                     

    D)        None of these

    Correct Answer: B

    Solution :

    [b] We have \[0<x<\pi /4\] \[0<x<0.8\] [x]=0 \[\int\limits_{0}^{\pi /4}{\left[ sinx.d(x- \right[x])}\] \[=\int\limits_{0}^{\pi /4}{sinx.d\left( x-0 \right)}\] \[=-(cosx)_{0}^{\pi /4}\] \[=1-\frac{1}{\sqrt{2}}\]


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