# Double Integral of an absolute value function - Need Help

Hi! Need help in solving this double integral:

1 1
∫ ∫ |x-y| dydx
0 0

Thanks in anticipation.

Regards,
Aby.

pasmith
Homework Helper
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).

Last edited:
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