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If z\neq 0, then \int_{0}^{100}\left [ arg\left | z \right | \right ]dx is          ? (where [.] denotes the greatest integer function)

  • Option 1)

    0

  • Option 2)

    10

  • Option 3)

    100

  • Option 4)

    undefined

 

Answers (1)

best_answer

As we learnt

Properties of Definite Integration -

For periodic function

Let Period (T) then

\int_{0}^{nT}f(n)dx= n\int_{0}^{T}f(x)dx

 

- wherein

Where f(x) is periodic function with period T and n is any integer.

 

 

\because \left | z \right | = real and positive, imaginary part is zero

            \therefore \arg \left | z \right |=0

            \therefore\left [ \arg \left | z \right | \right ]=0

            \therefore\int_{0}^{100}\left [ \arg \left | z \right | \right ]dx=\int_{0}^{100}0.dx=0


Option 1)

0

Option 2)

10

Option 3)

100

Option 4)

undefined

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Plabita

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