Results 1 to 4 of 4

Math Help - integral of an absolute value function

  1. #1
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3

    integral of an absolute value function

    Say you want to evaluate  \int^{2}_{0} \int^{1}_{0} |x-y| \ dx \ dy

    That's equivalent to evaluating  \int^{1}_{0} \int^{1}_{y} (x-y) \ dx \ dy \ + \int^{1}_{0} \int ^{2}_{x} (y-x) \ dy \ dx , right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Quote Originally Posted by Random Variable View Post
    Say you want to evaluate  \int^{2}_{0} \int^{1}_{0} |x-y| \ dx \ dy

    That's equivalent to evaluating  \int^{1}_{0} \int^{1}_{y} (x-y) \ dx \ dy \ + \int^{1}_{0} \int ^{2}_{x} (y-x) \ dy \ dx , right?
    Yes but it would be more simple to write it

     \int^{1}_{0} \int^{x}_{0} (x-y) \ dy \ dx \ + \int^{1}_{0} \int ^{2}_{x} (y-x) \ dy \ dx
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    What it the limits of integration were the following:

    \int^{3}_{\text{-}2} \int^{2}_{\text{-}1} |x-y| \ dx \ dy

    Can that be integrated exactly?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    This is the same way to proceed

     \int^{2}_{-1} \int^{x}_{-2} (x-y) \ dy \ dx \ + \int^{2}_{-1} \int ^{3}_{x} (y-x) \ dy \ dx
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 1st 2011, 10:56 PM
  2. Replies: 3
    Last Post: September 6th 2011, 10:45 AM
  3. Replies: 1
    Last Post: July 2nd 2011, 01:35 PM
  4. Replies: 3
    Last Post: September 21st 2010, 04:49 PM
  5. Replies: 2
    Last Post: November 8th 2009, 02:52 PM

Search Tags


/mathhelpforum @mathhelpforum