# (Slightly OT) Multiple integrals in LaTeX

1. Sep 14, 2006

### Muzza

How do you make the limits in a triple integral look okay? I need to write something like:

$$\iiint_{x \geq 3, y \geq 4, z \geq 5, 2z - x \geq 5} f(x, y, z)\, dx\,dy\,dz$$

but it looks kind of silly right now.

2. Sep 14, 2006

### Galileo

If you use \ limits_{down}^{up} you can get the text 'down' and 'up' above and below the integral signs. Also works for summation symbols.

$$\iiint \limits_{x \geq 3, y \geq 4, z \geq 5, 2z - x \geq 5} f(x, y, z)\, dx\,dy\,dz$$

But it still looks crappy.

$$\iiint \limits_{R} f(x, y, z)\, dx\,dy\,dz$$
where
$$R=\{(x,y,z)|x \geq 3, y \geq 4, z \geq 5, 2z - x \geq 5\}$$

Last edited: Sep 14, 2006
3. Sep 14, 2006

### Muzza

You're right. I'm probably better off just defining some set S = {(x, y, z); x >= 3, blah} and taking the integral over S.

4. Sep 14, 2006

### HallsofIvy

I'm wondering what in the world you mean! You want to take an integral over $x\ge 3$ but no upper limit on x? That just doesn't make sense.

If you want something like
$$\int_{x=3}^{5}\int_{y= 4}^{5- x}\int_{z=5}^{x+ y}f(x,y,z)dzdydx$$
click on the LaTex to see how it is done.

5. Sep 14, 2006

### Muzza

It's an improper integral. But this is all beside the point, I don't actually want to compute this particular integral. It was just an example I pulled out of thin air to illustrate my point.

Last edited: Sep 14, 2006
6. Sep 14, 2006

### shmoe

You should be able to stack the conditions in the limit:

$$\iiint \limits_{\substack{x \geq 3,\\ y \geq 4,\\ z \geq 5,\\ 2z - x \geq 5}} f(x, y, z)\, dx\,dy\,dz$$

ok, not very nice as-is, but multiline limits should give more flexibility.

7. Sep 14, 2006

### chroot

Staff Emeritus
Why not just give each integral sign -- say, the one for the variable x -- a lower limit of 3 and an upper limit of infinity?

- Warren

8. Sep 15, 2006

### Muzza

Again, the limits in my original post were just examples. There are situations where it's difficult or even impossible to write down the iterated integral, hence the need for descriptions like those in my first post.