Double Integral of an absolute value function - Need Help

[abubakar_mcs]

Hi! Need help in solving this double integral:

1 1
∫ ∫ |x-y| dydx
0 0


Thanks in anticipation.

Regards,
Aby.

 

[pasmith]

Hi! Need help in solving this double integral:

1 1
∫ ∫ |x-y| dydx
0 0


Thanks in anticipation.

Regards,
Aby.

$$\int_0^1 |x - y|\,dy = \int_0^x |x - y|\,dy + \int_x^1 |x - y| \,dy$$

 

[mathman]

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).

 

[abubakar_mcs]

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

 

[arildno]

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