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Have i made a correct presumption

  1. Apr 17, 2009 #1
    i am asked about convergance/divergance of the integral (from 0 to 1)

    [tex]\int[/tex]dx/ln(x)

    i say that
    t=lnx
    x=et
    dt=dx/x

    [tex]\int[/tex](et/t)dt ( from -infinity to 0 )

    now there is no way i have found to actuallt solve this integral,
    but i do know that in number series' there is a rule that if {lim(n->inf)An not= o} then the series diverges for sure,

    so i split my integral up so i get
    [tex]\int[/tex](et/t)dt ( from -infinity to -1 ) + [tex]\int[/tex](et/t)dt ( from -1 to 0 )

    now there is no problem at -1, so i checked the lims at 0 and -inf

    lim et/t = -infinity
    t->0

    lim et/t = 0
    t->-inf

    so from here i concur that even though the integral MIGHT converge at -inf, it CANNOT converge at 0, therefore the integral diverges.

    is this correct?? the end answer is correct 100% but i am asking about my method.
     
  2. jcsd
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