# Double Integral of an absolute value function - Need Help

1. Oct 9, 2013

### abubakar_mcs

Hi! Need help in solving this double integral:

1 1
∫ ∫ |x-y| dydx
0 0

Thanks in anticipation.

Regards,
Aby.

2. Oct 9, 2013

### pasmith

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

3. Oct 9, 2013

### 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: Oct 9, 2013
4. Oct 9, 2013

### abubakar_mcs

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

5. Oct 9, 2013

### arildno

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