Results 1 to 4 of 4

Math Help - Integrals problem 1

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Integrals problem 1

    Let f and h be two integrable functions in [a,b]. Let M=sup|f(x)| when x in [a,b].

    Prove that:
    | int{f(x)*h(x)}dx | <=M*int{| h(x) |}dx

    (The both integrals are from a to b)
    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
    We have \left|\int_a^bf\left(x\right)g\left(x\right)dx \right|\leq \int_a^b\left|f\left(x\right)g\left(x\right)\right  | dx  =\int_a^b\left|f\left(x\right)\right|\left|g\left(  x\right)\right| dx \leq \int_a^bM\cdot \left|g\left(x\right)\right| dx
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    May you please do it by Reimann or Darboux sums?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Also sprach Zarathustra View Post
    Let f and h be two integrable functions in [a,b]. Let M=sup|f(x)| when x in [a,b].

    Prove that:
    | int{f(x)*h(x)}dx | <=M*int{| h(x) |}dx

    (The both integrals are from a to b)
    What's wrong with what he did?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integrals problem...
    Posted in the Calculus Forum
    Replies: 0
    Last Post: May 8th 2010, 04:19 AM
  2. Integrals problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 30th 2010, 12:13 AM
  3. Integrals problem 1
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 20th 2010, 03:13 PM
  4. Integrals problem 2
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 8th 2010, 05:41 AM
  5. Integrals problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 30th 2010, 10:03 AM

Search Tags


/mathhelpforum @mathhelpforum