Double Integral of an absolute value function - Need Help

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Discussion Overview

The discussion revolves around solving a double integral involving the absolute value function |x-y| over the region defined by 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Participants are seeking assistance with the integration process and the appropriate limits for the integrals.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • Aby requests help with the double integral of |x-y| over the specified limits.
  • Aby proposes a breakdown of the integral into two parts based on the condition of y relative to x.
  • Some participants suggest changing |x-y| to x-y for y < x and to y-x for y > x, leading to two separate integrals.
  • Aby seeks clarification on how to express the new limits of integration after the transformation.
  • Another participant confirms the approach of splitting the y-interval into two segments: from 0 to x and from x to 1.

Areas of Agreement / Disagreement

Participants generally agree on the method of splitting the integral based on the relationship between x and y, but there is no consensus on the exact expression of the new limits or the final form of the integrals.

Contextual Notes

There are unresolved questions regarding the correct limits of integration after the transformation of the absolute value function, and participants have not fully clarified the mathematical steps involved.

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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