1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Improper Integrals

  1. Jan 26, 2007 #1
    1. The problem statement, all variables and given/known data

    Evaluate the following improper integrals of explain why they don't converge.
    Integral from 0 to infinity(1/the cubed root of x)dx
    I'm not sure how to make forulas, so this is the best I can do:
    0∫∞ (1/(3∙√x))dx

    2. Relevant equations

    No equations

    3. The attempt at a solution

    I know that when there is ∞ as an upper bound, the intergration is changed to:

    lim as b→∞ 0∫b (1/(3∙√x))dx
    But in this form, the 0 is a problem.

    and if the lower bound, 0, causes the function to be undefined, the integration is changed to:

    lim as a→0+ a∫∞ (1/(3∙√x))dx
    But, in this for the infinity is still a problem.


    Is there any way to combine the two so I can solve this.
    Any help is appreciated.
     
  2. jcsd
  3. Jan 26, 2007 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Well, the first thing you had better do is actually write out the anti- derivative!
    What is [tex]\int \frac{1}{^3\sqrt{x}}dx= \int x^{-\frac{1}{3}}dx[/tex]?

    Does it converge as x goes to 0? What happens as x goes to infinity?

    Oh, and notice that the problem specifically asks you to "explain why they don't converge". Maybe the problem you are having isn't really a problem!
     
    Last edited: Jan 26, 2007
  4. Jan 26, 2007 #3

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Is there anything wrong with the most obvious approach: make both changes?
     
  5. Jan 26, 2007 #4
    The anti- derivative is X^(2/3)
    2/3
    As x goes to infinity, the anti-derivative goes to infinity.
    As x goes to 0, the anti- derivative goes to 0.

    so, would I evaluate it as (infinity - 0), which is infinity, therefore it diverges.

    Is this right?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Improper Integrals
  1. Improper Integral (Replies: 5)

  2. Improper Integrals (Replies: 3)

  3. Improper integrals (Replies: 5)

  4. Improper integrals (Replies: 2)

  5. Improper Integral (Replies: 7)

Loading...