Results 1 to 5 of 5

Math Help - integral proofing

  1. #1
    Junior Member
    Joined
    Oct 2012
    From
    uk
    Posts
    41

    integral proofing

    let f(x,t)=xe^(-xt).show that the integral I(x)=∫f(x,t)dt (integration from 0 to infinite)exists for all x>=0 . is x->I(x) continuous on [0,infinite)
    what should i use here to prove the integral exist ???can someone give me the detail expanlation???
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1

    Re: integral proofing

    Quote Originally Posted by cummings123321 View Post
    let f(x,t)=xe^(-xt).show that the integral I(x)=∫f(x,t)dt (integration from 0 to infinite)exists for all x>=0 . is x->I(x) continuous on [0,infinite) what should i use here to prove the integral exist ???can someone give me the detail expanlation???
    \int_0^\infty  {xe^{ - xt} dt}  = \lim _{b \to \infty } \left( {\left. { - e^{ - xt} } \right|_{t = 0}^{t = b} } \right)=\lim _{b \to \infty } \left( {1 - e^{-xb} } \right) = ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2012
    From
    uk
    Posts
    41

    Re: integral proofing

    thank you,then the limit is 1 so the integral exists,but how about the continuous part, for now x->I(x) ,I(X)=1 it seems ,it is continuous?? i am not sure
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1

    Re: integral proofing

    Quote Originally Posted by cummings123321 View Post
    thank you,then the limit is 1 so the integral exists,but how about the continuous part, for now x->I(x) ,I(X)=1 it seems ,it is continuous?? i am not sure
    Frankly, I have the same question about I(x).
    We know that I(x)\ge 0. But I have no idea how it fits into the question.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Mar 2010
    Posts
    993
    Thanks
    244

    Re: integral proofing

    Isn't I(x)=1 for x>0 and I(x)=0 for x=0? So it would be continuous on (0,\infty) and discontinuous at 0, right?

    - Hollywood
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Joint density proofing
    Posted in the Statistics Forum
    Replies: 3
    Last Post: October 17th 2012, 02:34 AM
  2. Proofing
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 4th 2010, 05:49 AM
  3. Proofing no solution
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 7th 2009, 07:45 AM
  4. Proofing Divisors
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: January 20th 2009, 08:34 AM
  5. trig proofing
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 1st 2007, 06:18 AM

Search Tags


/mathhelpforum @mathhelpforum