(Slightly OT) Multiple integrals in LaTeX

[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.

 

[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.

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

 

[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.

 

[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.

 

[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.

 

[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.

 

[chroot]

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

 

[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.