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Use comparison theorem to determine if \int_{0}^{1}\frac{e^{-x}}{\sqrt{x}}~dx

  1. Feb 12, 2012 #1
    1. The problem statement, all variables and given/known data
    The question says use the comparison to determine if ##\int_{0}^{1}\frac{e^{-x}}{\sqrt{x}}dx## converges. What should I compare to?

    2. Relevant equations


    3. The attempt at a solution
     
    Last edited: Feb 12, 2012
  2. jcsd
  3. Feb 12, 2012 #2

    Dick

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    Hi tm5501987. Try using [ /tex] with a forward slash and no space. [tex]\int_{0}^{1}\frac{e^{-x}}{\sqrt{x}}dx[/tex]
    [itex]e^{-x}[/itex] is bounded between 1 and 1/e on [0,1], right?
     
  4. Feb 12, 2012 #3
    I am lost, not sure how that gets me to something I can compare to.
     
  5. Feb 12, 2012 #4

    Dick

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    [itex]\int_{0}^{1}\frac{e^{-x}}{\sqrt{x}}dx \lt \int_{0}^{1}\frac{1}{\sqrt{x}}dx[/itex]. Not so?
     
  6. Feb 12, 2012 #5
    Got it, thanks
     
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