Thread: Integral from negative infinity to positive infinity?

Is this correct?




Thanks in advance!

It does not equal infinity. But if you meant that it diverges, then yes, it does.

I would think it is undefined? My teacher said it is equal to infinity because 5x approaches to positive infinity faster than x approaches to negative infinity and I did not agree because it comes out to be infinity minus infinity.
If it is not undefined, what is it? If it is undefined, how could I better express to my teacher that they're incorrect?

Originally Posted by m84uily

Is this correct?




Thanks in advance!

Integrals can be broken into pieces, so:



If then you can reduce that to , which obviously diverges.

(Edit: Sorry, forgot to divide by 2.)

Originally Posted by MagiMaster

Integrals can be broken into pieces, so:



If then you can reduce that to , which obviously diverges.

Which is undefined? Maybe I'm misunderstanding the word "divergent" I take it to mean that the sums do not approach some limit. If that's right then I understand its being divergent, I just want to know if my teacher's reasoning is incorrect or not.

Your teacher isn't exactly wrong, just not exactly accurate. It'd be more proper to say that:


Infinities generally don't make much sense outside of limits, so without being more precise, it'd be hard to say for sure what's right or wrong.

Originally Posted by MagiMaster

Your teacher isn't exactly wrong, just not exactly accurate. It'd be more proper to say that:


Infinities generally don't make much sense outside of limits, so without being more precise, it'd be hard to say for sure what's right or wrong.

Okay! Thanks :-D

I believe all parties here, including your teacher, do not understand the meaning of the phrase

.

What this means is that



as and independently of each other. It is not sufficient to set a = -b and take the limit.

In this particular example, the integral is undefined.

Originally Posted by m84uily

I would think it is undefined? My teacher said it is equal to infinity because 5x approaches to positive infinity faster than x approaches to negative infinity and I did not agree because it comes out to be infinity minus infinity.
If it is not undefined, what is it? If it is undefined, how could I better express to my teacher that they're incorrect?

salsaonline, unsurprisingly, is correct.

So are you.

Are you taking a high-school calculus class ? If so, there is probably little that you can do to convince your teacher. If not, find a better college.

You will see such questions treated properly, and in some depth, in a university class on real analysis. If the integrand is non-negative, things are fairly simple. If not, the issues can be subtle.

Originally Posted by DrRocket

Originally Posted by m84uily

I would think it is undefined? My teacher said it is equal to infinity because 5x approaches to positive infinity faster than x approaches to negative infinity and I did not agree because it comes out to be infinity minus infinity.
If it is not undefined, what is it? If it is undefined, how could I better express to my teacher that they're incorrect?

salsaonline, unsurprisingly, is correct.

So are you.

Are you taking a high-school calculus class ? If so, there is probably little that you can do to convince your teacher. If not, find a better college.

You will see such questions treated properly, and in some depth, in a university class on real analysis. If the integrand is non-negative, things are fairly simple. If not, the issues can be subtle.

Yeah, I'm in high school, I guess I'll give up on trying to convince my teacher and just do things their way for marks. I'll be looking forward to that class on real analysis :-D