the integral is 1/((x-5)^2/3) from -infinity to +infinity. I ended up with (-infinity) + (+infinity) = 0 , is this correct? and is this convergent? tks.
2006-09-20 02:33:43 · 6 answers · asked by Black C 1 in Science & Mathematics ➔ Mathematics
For improper integrals like this, you have to do separate integrals on each side of the singularity. This one has a singularity at x=5, so you have to do one integral from -infty to 5 and another from 5 to +infty. Both of these integrals diverge, so the whole thing diverges. In fact, if *either* of the partial integrals diverges, we say that the whole thing diverges.
A more fundamental problem is that you cannot use anti-derivatives to do integrals across a singularity. So when you did the integral of (x-5)^(-2/3), you *must* break it up at x=5 or you may very well get the wrong answer. If you try it with 1/x^2 from x=-1 to x=1, and look at the graph, you will see that the area has to be positive, but the anti-derivative method gives a negative answer.
Finally, if you get a result in any problem like infty-infty, it simply says you have to do *more work*. Such a limit is an indeterminant form, which means the answer can come out to be anything.
2006-09-20 08:18:08 · answer #1 · answered by mathematician 7 · 2⤊ 0⤋
First off, I don't think you should get infinity - infinity, but even if you did, it is not 0, it is indeterminate. It depends on what the limit really is whether it has an answer or not. X - X as X goes to infinity is 0 (stupid example, but maybe you'll see my point).
To do these kind of integrals, you can go -infinity to 0 and then 0 to infinity, and add them together. If I did my math right, it does not converge.
2006-09-20 03:52:09 · answer #2 · answered by An electrical engineer 5 · 1⤊ 0⤋
Infinity is not a number it is a concept. Infinity includes everything. Suggesting a negative infinity would imply infinity in the opposite direction and infinity has no beginning or end. Negative infinity is meaningless.
2006-09-20 02:48:43 · answer #3 · answered by » mickdotcom « 5 · 1⤊ 1⤋
Infinity is not a 'real' number, so no calculations using it have any real meaning.
2006-09-20 02:38:59 · answer #4 · answered by Anonymous · 1⤊ 1⤋
I get + Inf + Inf which would be divergent.
2006-09-20 06:31:27 · answer #5 · answered by Mariko 4 · 0⤊ 0⤋
Don't listen to those boobs. It is convergent.
2006-09-20 03:29:24 · answer #6 · answered by Anonymous · 0⤊ 1⤋