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!

Limitsproving they exist?

  1. Apr 25, 2004 #1
    limits..proving they exist???

    Wot do u have to do to prove that an intergral exists.?? I know how to do it if the integrals bounds are given ( example, [a,b]) but wot if the integral is from x till infinity??
     
  2. jcsd
  3. Apr 25, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    In the same wasy as infinite sums, work out the integral from a to b and then let b tend to infinity. Eg
    integral of 1/x from a to b is log(b) - log(a), which tends to infinity as b tends to infinity so the integral doesn't exist.
    integral of 1/x^2 from a to be is 1/a^2-1/b^2, which tends to 1/a^2 as b tends to infinity so the infinite integral exists.

    If you wish to integrate from minus infinity to infinity, you must do the integral from a to b and let a and b tend to infinity independently.

    Thus the improper integral of sin(x) over the real line does not exist even though you can choose the interval to be [-a,a] and get an answer of zero (other choices will give different answers hence the integral does not exist)
     
  4. Apr 25, 2004 #3
    How will you do
    [tex]\int\frac{sinx}{x}dx[/tex]
    from zero to infinity.
    Which can be written as a alternating series
    T subscript n =[tex]\mid\int\frac{sinx}{x}dx\mid[/tex] over intervals ([tex](n-1)\pi,n\pi[/tex])
    but how do show as n tends to infinity that T(n) tends to 0???
    cos i cant integrate it
     
    Last edited: Apr 25, 2004
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Limitsproving they exist?
Loading...