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Double Integral of an absolute value function - Need Help

  1. Oct 9, 2013 #1
    Hi! Need help in solving this double integral:

    1 1
    ∫ ∫ |x-y| dydx
    0 0

    Thanks in anticipation.

  2. jcsd
  3. Oct 9, 2013 #2


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    \int_0^1 |x - y|\,dy = \int_0^x |x - y|\,dy + \int_x^1 |x - y| \,dy
  4. Oct 9, 2013 #3


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    Change |x-y| to x-y for y < x. Change |x-y| to y-x for y > x.
    You now have two double integrals which you can do easily (y integral inner for both).
    Last edited: Oct 9, 2013
  5. Oct 9, 2013 #4
    Thanks mathman, but how to write the new expression i.e. how to change the limits of the integral...??? Is the one I wrote below right??

    11 11
    ∫∫ (x-y) dydx + ∫∫ (y-x) dydx
    00 00
  6. Oct 9, 2013 #5


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    Dearly Missed

    Split the y-interval into 0 to x, and x to 1, as pasmith showed
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