Double integral with absolute value of x-y

[Goalie_Ca]

int(int(abs(x-y)*6*x^2*y)) the range of x and y are 0,1. Normally i'd check to split it up and change the limits, but i think my brain is broken because I'm not seeing it at the moment.

simple question that i need to know how to do for stats without using maple :P

 

[Hurkyl]

Well, try restating what you're trying to do. You're specifically interested in breaking things up based on |x - y|, so consider that all by itself... what are the pieces? How do you identify which piece a point is in?

 

[Goalie_Ca]

edit: I think i got it now. I plotted the abs function in 3d in maple. that helped.

Lol, why did i double it again? I should have just added both parts!

> int(int(abs(x-y)*6*x^2*y,x=0..1),y=0..1);
* * * * * * * * * * * * * * * 1
* * * * * * * * * * * * * * * -
* * * * * * * * * * * * * * * 4
> int(int((x-y)*6*x^2*y,y=0..x),x=0..1);
* * * * * * * * * * * * * * * 1
* * * * * * * * * * * * * * * -
* * * * * * * * * * * * * * * 6
> int(int((y-x)*6*x^2*y,x=0..y),y=0..1);
* * * * * * * * * * * * * * * 1 
* * * * * * * * * * * * * * * --
* * * * * * * * * * * * * * * 12