# Supposedly simple double integral

1. Nov 3, 2007

### raynoodles

double integral of xy dA
in the triangular region of (0,0), (3,0), (0,1).
my problem that I am having is finding the limits I am suposed to find dx or dy in. I figure I should use 0 to 3 for dx, but then i do dy from 0 to what? Help appreciated.

2. Nov 3, 2007

### Avodyne

Try drawing a picture of the region. Then, for a given value of x, what values of y lie within the region? This gives you the limits of integration for y, given x. (Of course, you must then do the y integral before you do the x integral.)

3. Nov 3, 2007

### raynoodles

so then the parameters for y would be: 0 to x/3?

4. Nov 4, 2007

### HallsofIvy

Staff Emeritus
Yes, because the upper boundary is the line y= x/3.

It is a very good exercise to "swap" the limits of integration. Suppose you wanted to integrate with respect to x first and then y? Clearly to cover the entire triangle, you must take y going from 0 to 1. For each y, then, x must go from the left boundary, x= 0, to the "right" boundary which is still that line y= x/3. That is, x must go from x= 0 to x= what? Do the integral of xy both ways and see if you get the same thing.

5. Nov 4, 2007

### raynoodles

still not getting the right answer.

I used the parameters dy= 0 to 1 and dx= 0 to -3y+3 and got 2.375.