# Confused with double integral

1. Jan 31, 2006

### denian

given f(x,y) = x-y

R is a triangle with vertices (2,9), (2,1), (-2,1)
then i need to find I,

I = int. int. (x-y) dx dy

i was taught to use this range when i do the dbl. integration
1 <= y <= 9

(y-5)/2 <= x <= 2

i want to ask, why can't i use this range:

1 <= y <= 9

-2 <= x <= (y-5)/2

thank you.

2. Jan 31, 2006

### TD

Try making a graphic, you'll see that with your ranges, you're covering the 'other triangle' when you complete the rectangle (by adding the point (-2,9))

Last edited: Jan 31, 2006
3. Jan 31, 2006

### denian

Oh, thank you, TD!!

4. Jan 31, 2006

### TD

You're welcome! It's always handy to make a fast sketch of the problem, it makes it a lot easier to determine the ranges if you 'see' the area rather than trying to do it with the equations only.

5. Jan 31, 2006

### denian

i got confused again.

do you mean (-2,9)??

6. Jan 31, 2006

### TD

Yes of course, for that rectangle I mentioned

I'll correct, thanks.