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\int_{-1}^{10}sgn(x-\left [ x \right ])dx equals   [here [.] denotes greatest integer function]

  • Option 1)

    10

  • Option 2)

    11

  • Option 3)

    9

  • Option 4)

    11/2

 

Answers (1)

best_answer

As we learnt

Properties of Definite Integration -

If f(x) is a periodic function with period T then \int_{a}^{a+T}f(x)dxis independent of a.

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We have, sgn\left ( x-\left [ x \right ] \right )= \begin{Bmatrix} 1,if\: x \: is\: not\: an\: integer\\ 0,if\: x \: is\: \: an\: integer \end{Bmatrix}

                       Hence,  \int_{-1}^{10}sgn\left ( x-\left [ x \right ] \right )dx= 11\left ( 1-0 \right )=11.


Option 1)

10

Option 2)

11

Option 3)

9

Option 4)

11/2

Posted by

gaurav

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