# Thread: Simplifying a tripple integral

1. ## Simplifying a tripple integral

Hello, I am trying to solve an integral but it quickly gets crowded with too many terms... (once you start solving it you'll see what I mean) I was wondering if there is a way to make computations simpler.
$\displaystyle \int^1_0\int^{1-u}_0\int^{1-u-v}_0 8uvw\,dw\,dv\,du$

2. ## Re: Simplifying a tripple integral

Originally Posted by nuebie
Hello, I am trying to solve an integral but it quickly gets crowded with too many terms... (once you start solving it you'll see what I mean) I was wondering if there is a way to make computations simpler.
$\displaystyle \int^1_0\int^{1-u}_0\int^{1-u-v}_0 8uvw\,dw\,dv\,du$
Without seeing your work how can we tell if you could have done it easier? It looks straightforward enough, just polynomials.

3. ## Re: Simplifying a tripple integral

Hi, yes it's pretty straightforward. It goes like:
$\displaystyle \int^1_0\int^{1-u}_0\int^{1-u-v}_0(8uvw)\mbox{ }dw\,dv\,du = \int^1_0\int^{1-u}_0 4uv\Big[w^2\Big]^{1-u-v}_0 \mbox{ }dv\,du = \int^1_0\int^{1-u}_0 4uv(1-u-v)^2 \mbox{ }dv\,du$
so far so good and as soon as you start expanding it becomes long and ugly, then you integrate again and get even more terms. I mean, it's not difficult but tedious and it's easy to make accidental mistakes. That's why I was asking for a more compact way to do it.

4. ## Re: Simplifying a tripple integral

Yes, it's pretty much grunt work. Once you understand integration such problems are a waste of time. If you decide to push it through to the end, the answer is $\frac 1 {90}$ if that is any help. I let Maple do the grunt work.

5. ## Re: Simplifying a tripple integral

Originally Posted by Walagaster
Yes, it's pretty much grunt work. Once you understand integration such problems are a waste of time. If you decide to push it through to the end, the answer is $\frac 1 {90}$ if that is any help. I let Maple do the grunt work.
I agree that it's a waste of time, but I need this one for an assignment problem, so I guess I gotta get through it Thank you!