Results 1 to 7 of 7
Like Tree2Thanks
  • 1 Post By Plato
  • 1 Post By Plato

Math Help - Riemann Lebesgue integrals

  1. #1
    Member kezman's Avatar
    Joined
    Jul 2006
    Posts
    93
    Thanks
    2

    Riemann Lebesgue integrals

    Im having some trouble with these ones

    Decide if the following integrals exist as Lebesgue integrals and as Riemann integrals

    \int_{1}^{+ \infty} \frac{dx}{x^2}

    \int_{0}^{+ \infty} \frac{sen^2(x)dx}{x^2}

    Thanks!!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1

    Re: Riemann Lebesgue integrals

    Quote Originally Posted by kezman View Post
    Decide if the following integrals exist as Lebesgue integrals and as Riemann integrals

    \int_{1}^{+ \infty} \frac{dx}{x^2}

    \int_{0}^{+ \infty} \frac{sen^2(x)dx}{x^2}
    Are they Riemann integrable? If not why not?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member kezman's Avatar
    Joined
    Jul 2006
    Posts
    93
    Thanks
    2

    Re: Riemann Lebesgue integrals

    As for riemann integral the first one exist and is = -1
    The second one doesnt exist.

    The problem is to prove if exists the lebesgue integral, I have no clue.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1

    Re: Riemann Lebesgue integrals

    Quote Originally Posted by kezman View Post
    As for riemann integral the first one exist and is = -1
    The second one doesnt exist.
    The problem is to prove if exists the lebesgue integral, I have no clue.
    The value of the first is 1, not -1.
    For the second did you notice that \frac{\sin^2(x)}{x^2}\le\frac{1}{x^2}.
    Thanks from kezman
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member kezman's Avatar
    Joined
    Jul 2006
    Posts
    93
    Thanks
    2

    Re: Riemann Lebesgue integrals

    ok the second integral if exists must be between 0 and 1
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1

    Re: Riemann Lebesgue integrals

    Quote Originally Posted by kezman View Post
    ok the second integral if exists must be between 0 and 1
    Here is a reference for you.

    And another.
    Thanks from kezman
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member kezman's Avatar
    Joined
    Jul 2006
    Posts
    93
    Thanks
    2

    Re: Riemann Lebesgue integrals

    Excelent, so Ill have to fight against lebesgue integral.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rate of divergence of Lebesgue integrals.
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: February 10th 2011, 02:14 PM
  2. Riemann-Lebesgue
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 16th 2010, 02:19 PM
  3. Riemann-Lebesgue Lemma
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 11th 2009, 12:05 PM
  4. upper function and lebesgue integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 10th 2007, 03:02 PM
  5. Riemann Sums and Riemann Integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 1st 2006, 02:08 PM

Search Tags


/mathhelpforum @mathhelpforum