Double Integral of an absolute value function - Need Help

  • #1
Hi! Need help in solving this double integral:

1 1
∫ ∫ |x-y| dydx
0 0


Thanks in anticipation.

Regards,
Aby.
 

Answers and Replies

  • #2
pasmith
Homework Helper
2,004
638
Hi! Need help in solving this double integral:

1 1
∫ ∫ |x-y| dydx
0 0


Thanks in anticipation.

Regards,
Aby.

[tex]
\int_0^1 |x - y|\,dy = \int_0^x |x - y|\,dy + \int_x^1 |x - y| \,dy
[/tex]
 
  • #3
mathman
Science Advisor
7,932
484
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:
  • #4
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).

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
 
  • #5
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,970
134
Split the y-interval into 0 to x, and x to 1, as pasmith showed
 

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