Double Integral of an absolute value function - Need Help

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SUMMARY

The discussion focuses on solving the double integral of the absolute value function |x-y| over the region [0,1] x [0,1]. The integral can be expressed as two separate integrals: one for the case where y < x (|x-y| = x-y) and another for y > x (|x-y| = y-x). The correct approach involves splitting the integral into two parts with adjusted limits: ∫∫ (x-y) dydx from 0 to x and ∫∫ (y-x) dydx from x to 1. This method simplifies the calculation of the double integral.

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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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