Double Integral of an absolute value function - Need Help

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The discussion focuses on solving the double integral of the absolute value function ∫∫ |x-y| dydx over the region [0,1] x [0,1]. Participants suggest splitting the integral into two parts based on the conditions where y is less than or greater than x. The transformation involves changing |x-y| to x-y for y < x and to y-x for y > x, leading to two separate integrals. There is a request for clarification on how to properly express the new limits of integration after this transformation. The conversation emphasizes the importance of correctly setting up the integrals for accurate computation.
abubakar_mcs
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Hi! Need help in solving this double integral:

1 1
∫ ∫ |x-y| dydx
0 0


Thanks in anticipation.

Regards,
Aby.
 
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abubakar_mcs said:
Hi! Need help in solving this double integral:

1 1
∫ ∫ |x-y| dydx
0 0Thanks in anticipation.

Regards,
Aby.

<br /> \int_0^1 |x - y|\,dy = \int_0^x |x - y|\,dy + \int_x^1 |x - y| \,dy<br />
 
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:
mathman said:
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
 
Split the y-interval into 0 to x, and x to 1, as pasmith showed
 

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