Results 1 to 2 of 2

Math Help - Showing that a finction is not integrable

  1. #1
    Newbie
    Joined
    Jan 2011
    Posts
    24

    Showing that a finction is not integrable

    Hello!

    I've got what looks like a simple problem but I just can't get it right.

    Here it goes: Show that f(x)=d/dx (x^2\sin x^{-3}), x>0, is not in L^1(0,1).

    My first thought was to simply compute the integral
    \int_{0}^{1}|f(x)|dx and show that it diverges - however I had no luck doing that.

    Then I thought that I might simply estimate it from below with something that I know is infinite but no luck there either, all I got was:
    \int_{0}^{1}|2x\sin x^{-3}-3x^{-2}\cos x^{-3}|dx \geq \int_{0}^{1}(|2x\sin x^{-3}|-|3x^{-2}\cos x^{-3}|)dx

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    678
    Thanks
    32

    Re: Showing that a finction is not integrable

    You don't need to compute the integral. Just notice that \sin (x^{-3})\overset{0}{\sim} x^{-3} and the integral \int_0^1\frac 1xdx is divergent.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. f & g Riemann integrable, show fg is integrable
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: February 12th 2011, 10:19 PM
  2. f is integrable
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: January 31st 2011, 02:31 PM
  3. Is a bounded integrable function square integrable?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 28th 2010, 07:26 PM
  4. Prove that if f is integrable then kf is integrable.
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: March 9th 2010, 01:35 PM
  5. [SOLVED] f integrable implies f^2 integrable
    Posted in the Differential Geometry Forum
    Replies: 15
    Last Post: June 8th 2009, 11:53 PM

Search Tags


/mathhelpforum @mathhelpforum