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Math Help - step function integration

  1. #1
    Newbie omeganeu's Avatar
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    step function integration

    Hi

    can I say that s(x-a)dx=a where s is the step function of (x-a) and the integration is from zero to infinity.
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  2. #2
    MHF Contributor

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    No, you can't! s(x-a) is equal to 0 from negative infinity to a, 1 from a to infinity.

    \int_{-\infty}^{\infty}s(x-a)dx= \int_a^\infty dx
    which does not exist.
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  3. #3
    Newbie omeganeu's Avatar
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    but I mean by this step function that it is equall one in the region from zero to a, and it is equall zero in all the regions less than zero and greater than a, so I quessed that its integration from zero to infinity will be reduced to the interval where it is equall one (from zero to a). I thought of it as a multiplication by zero (which gives zero) in all regions except when x goes from zero to a.
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  4. #4
    Newbie omeganeu's Avatar
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    s(x-a)dx=a

    actually I need to integrate (from zero to infinity) a function which is equall one in the region from 0 th a and equalls zero otherwise (when x less than zero or greater than a).
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  5. #5
    MHF Contributor

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    In that case, it is, of course, \int_0^a dx= a, as you had originally.
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  6. #6
    Newbie omeganeu's Avatar
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    Thanks a lot this solve a great problem to me.
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