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Homework Help: Divergent or Convergent?

  1. Mar 7, 2006 #1

    Aki

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    I want to know if the integral

    [tex]\int_0^{\infty} dx/(4x^3 + x^(1/3)) [/tex]

    is convergent or divergent?


    Thanks
     
    Last edited: Mar 7, 2006
  2. jcsd
  3. Mar 7, 2006 #2

    shmoe

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    What have you tried? Have you compared it with integrals whose convergece/divergence you know? Keep in mind your integrand is also undefined at 0.

    Use {} instead of () to group things in latex, click on [tex]\int_{0}^{\infty}[/tex]
     
  4. Mar 7, 2006 #3

    Aki

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    Well I'm just not sure what happens when

    [tex]\int_{0}^{1}dx/x^{1/3}[/tex]

    I think it converges, but I"m not too sure.
    because when that function is below [tex]1/x[/tex] on the graph
     
    Last edited: Mar 7, 2006
  5. Mar 8, 2006 #4

    HallsofIvy

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    What is the anti-derivative of [itex]\frac{1}{x^{\frac{1}{3}}}= x^{-\frac{1}{3}}[/itex]
     
    Last edited by a moderator: Mar 9, 2006
  6. Mar 9, 2006 #5

    dextercioby

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    Is the function [itex]\frac{1}{4x^{3}+x^{1/3}} [/itex] ? If so, what is its limit to [itex] 0^{+} [/itex] ?

    Daniel.
     
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