Results 1 to 4 of 4

Math Help - Prove these integrals are equal

  1. #1
    Member
    Joined
    Mar 2009
    Posts
    168

    Prove these integrals are equal

    Prove that

    \int_{0}^\infty x^2 e^{{-x}^{2}}=\frac{1}{2} \int_{0}^\infty e^{{-x}^{2}}

    and both integrals converge.

    Any help on this? I tried doing integration by parts for the second one but couldn't reach an answer.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by paupsers View Post
    Prove that

    \int_{0}^\infty x^2 e^{{-x}^{2}}=\frac{1}{2} \int_{0}^\infty e^{{-x}^{2}}

    and both integrals converge.

    Any help on this? I tried doing integration by parts for the second one but couldn't reach an answer.
    see post #2 here
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Mar 2009
    Posts
    168
    That thread was really helpful!

    But now I'm trying to solve

    \int_0^\infty x^2e^{-x^2}dx by using the same method, and it's not working out so nicely. I've set it up the same way and converted it into polar, and now I'm at

    \int_0^\infty\int_0^{2\pi}r^5cos^2\theta sin^2\theta e^{-r^2}d\theta dr and I have a feeling that's not simple to evaluate... :-(

    Is there a simpler way to do this?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Mar 2009
    Posts
    168
    Actually, it can be done using integration by parts. Thanks for the link, still!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove me that pi is no equal 2
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 8th 2011, 10:40 AM
  2. Show two integrals are equal
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 15th 2011, 02:08 AM
  3. Prove two double integrals are equal
    Posted in the Calculus Forum
    Replies: 5
    Last Post: January 14th 2011, 01:11 AM
  4. Proof involving integrals equal to 0.
    Posted in the Calculus Forum
    Replies: 10
    Last Post: February 24th 2010, 12:48 AM
  5. prove H_T less than or equal to S_n
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 16th 2008, 03:59 PM

Search Tags


/mathhelpforum @mathhelpforum