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Like ∫(...)dx or ∫dx(...) ?
Just wondering ;).
Just wondering ;).
Exactly why I don't like it before - it's ambiguous to me.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.
∫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.
Well, the thing is, an integral is an operator. It needs to operate on something.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".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.
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.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.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.
That made my night. Thanks .[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: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##.
Here would be one place. The actual standard would probably be a better place.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.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".It seems the convention of placing the differential after the integrand has been around a long time.
Rabble-rouser![tex] \int_b^a\frac{1}{log(1)} dx[/tex]
You too!I prefer:
[tex]\int_{f(x)}^{dx}|_{a}^{b}[/tex]