- #1
PhysicsGente
- 89
- 3
Like ∫(...)dx or ∫dx(...) ?
Just wondering ;).
Just wondering ;).
collinsmark said:Usually this one:
[tex] \int_a^b \frac{1}{x^2} dx,[/tex]
but occasionally I might write it like this:
[tex] \int_a^b \frac{dx}{x^2}, [/tex]
although this is right out
[tex] \int_a^b dx\frac{1}{x^2}, [/tex]
unless I actually mean for the [itex] \frac{1}{x^2} [/itex] not to be integrated.
bp_psy said:∫dxf(x) has only one reasonable meaning that is (x+c)f(x). I am however using this unreasonable notation extensively when doing Qm since it is much better to be consistent with the notation you usually find in books.
1MileCrash said:I disagree, placing the dx next to the integral sign should mean the same thing. I don't think we have to necessarily view dx as the "end" or closure of the integral.
The way I see it in very non rigorous terms is that you can't chose to not integrate everything that has to do with x in an expression so dx is really "the end of the integral".1MileCrash said:I disagree, placing the dx next to the integral sign should mean the same thing. I don't think we have to necessarily view dx as the "end" or closure of the integral.
collinsmark said:Well, the thing is, an integral is an operator. It needs to operate on something.
With lots of other operators, there's different notation involved such as
[tex] \mathcal{O}\left\{ \frac{1}{x^2} \right\} [/tex]
and it's generally understood that the above notation is not necessarily equal to
[tex] \mathcal{O}\{1\}\frac{1}{x^2} [/tex]
or
[tex] \frac{1}{x^2}\mathcal{O}\{1\} [/tex]
Of course integrals are a little special, since there truly is a multiplication involved by the dx. But even so, if it's okay to scramble things up, would it also be appropriate to say that
[tex] \int_a^b \frac{1}{x^2}dx [/tex]
is the same thing as
[tex] \frac{1}{x^2} \int_a^b dx [/tex]
or worse yet,
[tex] dx \frac{1}{x^2} \int_a^b \ ?[/tex]
If the integral sign specifies the left of what must be integrated, what is to specify the right end? That's usually the job of the dx is my point.
Okay, fair enough. It just looks wrong though.1MileCrash said:No one said anything about moving the integration symbol itself, that is completely unrelated to what we are talking about. The integral sign is not a multiplicand; dx is, you said it yourself.
Look at our notation for the limit. There is no "closing" symbol, it's exactly the same thing. dx is not defined to be the end of an integral. To say that putting dx next to the integral sign is not ambiguous is just silly.
collinsmark said:[tex] dx \frac{1}{x^2} \int_a^b \ ?[/tex]
You bring up a good point, and I was wondering about that. There was a time where I would un-italicize the d when using it for a differential. But then I stopped, not so much because I was lazy, but rather because many others don't seem to do that. Even Wolfram mathworld uses italicized ds such as here:jhae2.718 said:I'm going to be pedantic and make the claim that the "d" should be typeset in Roman font; ##\mathrm{d}x## is a differential; ##dx## is the product of scalars ##d## and ##x##.
collinsmark said:You bring up a good point, and I was wondering about that. There was a time where I would un-italicize the d when using it for a differential. But then I stopped, not so much because I was lazy, but rather because many others don't seem to do that. Even Wolfram mathworld uses italicized ds such as here:
http://mathworld.wolfram.com/AbelsIntegral.html
And Wolfram isn't the only place. It seems pretty common.
So now I don't know what to think.
So where does one learn about such conventions anyway?
I'm not a fan. It's jarring to the eyes (my eyes, in any case). It just looks ugly. Extremely ugly.jhae2.718 said:I'm going to be pedantic and make the claim that the "d" should be typeset in Roman font; ##\mathrm{d}x## is a differential; ##dx## is the product of scalars ##d## and ##x##.
A long, long time. That's why I called it "archaic".Astronuc said:It seems the convention of placing the differential after the integrand has been around a long time.
ChiralWaltz said:[tex] \int_b^a\frac{1}{log(1)} dx[/tex]
arildno said:I prefer:
[tex]\int_{f(x)}^{dx}|_{a}^{b}[/tex]
I only use that one on Halloween.WannabeNewton said:I prefer ##\int dx\underset{dx}{\overset{dx}{f(x)}}dx##.
WannabeNewton said:I prefer ##\int dx\underset{dx}{\overset{dx}{f(x)}}dx##.
As a scientist, I typically write my diagnoses in a laboratory or research setting. This allows me to have access to necessary equipment and materials, as well as collaborate with other scientists.
Yes, I have a specific writing process for my diagnoses. I start by gathering all relevant data and research on the topic, then I analyze and interpret the data to come up with a diagnosis. Finally, I write up the diagnosis, making sure to include all necessary information and evidence to support my findings.
Accuracy is crucial in scientific diagnoses, so I take several steps to ensure it. I make sure to use reliable and validated research methods, consult with other experts in the field, and double-check my findings before finalizing my diagnosis.
I use a variety of tools and software to write my diagnoses, depending on the specific project. Some common tools I use include word processing software, statistical analysis programs, and data visualization tools. I also use reference management software to keep track of my sources and citations.
As a scientist, it is important to effectively communicate my diagnoses to others in the scientific community. I typically present my findings at conferences, publish them in scientific journals, and collaborate with other scientists to share and discuss my diagnoses. I also make sure to use clear and concise language to make my diagnoses easily understandable to a wider audience.