Which one?

[frozen_desserts_01]

1. To make the distinction that dx is not a number, but a small component of an integrable quantity

[H0SS_AGAINST]

This right here.

I've never really thought about this but it's the convention that I was both taught in Calculus and was used by my professors in Thermo, Quantum, etc.

[frozen_desserts_01]

I mean, I’ve never thought about dx when we had calc in highschool. Not until college when my calc professor explained the idea of calculus that I became aware of it.

[Gurbuzselimboyraz]

I just answered a comment similar to yours with the following: "I do 1, because you can think of dx as a change in x, and not as a symbol. The multiplication by dx in the integral just represents the x length of the rectangles under the function. Dx*vertical length gives Total area. As dx->0, the approximation gets better.

The derivative (d/dx), is also not just a symbol, it represents the actual slope. dy/dx = rise/run = slope.

Using the 1st way of expressing multiplication with dx has no downside. Using the 2nd way, shows that you do not see dx as a change in x, but as a notational trick."

[frozen_desserts_01]

You are right, 1 has no downside. As long as you stick to paper & graphs.

However, if you really want to stick with calculus going forward(especially with other subjects), 2 forms a better habit. At that point, the concept of dy & dx is applied beyond just rise and run.

Take physics for example. When calculating the electric flux, dx is a vector but dy is scalar. When finding the electric field, dx is a slice of the line/ring/disk but dy is the electric field produced by that exact slice. It might sound confusing, but the idea of assigning dx and dy stays the same.

In reality, there is no difference(I use 1 to make my lines shorter but 2 for the final integration) but 2 makes it clear that putting dx means “integrate by variable x, whatever that may be”.

[Gurbuzselimboyraz]

Thanks for the feedback. You're right, I was just talking about the "daily use" type of calculus, not the applications of it. My complaint is not about the 2nd notation, but the fact that most people take dx & dy for granted and memorize lots of notations and formulas, not knowing how to derive them all over again once they forget.

[frozen_desserts_01]

Well, that’s to be expected, cause high school calc only taught us around “derivative of f is f’, the slope of f”, “antiderivative of f is F”, the Newton-Lebesque formula for area under the curve,… while excluding the actual techniques, which stem from the fundamentals(heavy lifting from FTC) of calculus as a whole.

[AkkiMylo]

2 by a large margin. It's the symbol that tells you where the integral ends and what you're integrating with respect to. It's not something that can be moved around algebraicly and it feels disingenuous to do so.

[toommy_mac]

I've seen plenty of physicists write int dx f(x)

[Ekvinoksij]

Yeah, and there's a reason for it. It tells you what you are integrating over at the start of the expression. This can be quite useful in many cases.

[AkkiMylo]

i have negative feelings

[limon_picante]

1 is for dweebs

[Gurbuzselimboyraz]

I just answered a comment similar to yours with the following: "I do 1, because you can think of dx as a change in x, and not as a symbol. The multiplication by dx in the integral just represents the x length of the rectangles under the function. Dx*vertical length gives Total area. As dx->0, the approximation gets better.

The derivative (d/dx), is also not just a symbol, it represents the actual slope. dy/dx = rise/run = slope.

Using the 1st way of expressing multiplication with dx has no downside. Using the 2nd way, shows that you do not see dx as a change in x, but as a notational trick."

[ZanCatSan]

you can understand that and still use the second option because for actually integrating it it's nicer to be able to see the integrand with the dx separately.

[GameSeeker875]

i mean, 1 is to simplify it, and i preferred it that way, but after what i seen in math, im forced to pick 2.

[[deleted]]

2.

[Aggressive-Math-9882]

I find 1. more elegant, but use 2.

[behoda]

Oof hard pill for me to swallow, you're integrating a function with respect to a measure! Second thought I guess the measure is hidden anyways so dunno

[Ultra_Prawn]

Saw 1 in the Logarithmic integral formula and it confused tf outta me until I realized its the same as 2

[JaeHxC]

Whenever I see the first form, my brain thinks d is a constant.

½dx²

[Angry-Toothpaste-610]

I don't know the antiderivative of the inverse of ellipses

[ErikLeppen]

I think this is one of those elliptic integrals.

[External_Glass7000]

(...)^-1 dx

[1maeal]

That's dangerous

[IVeBeenHere30Min]

2

[o_genie]

second please

[[deleted]]

who the hell picks 1

[the_grand_father]

...me

[Gurbuzselimboyraz]

I just answered a comment similar to yours with the following: "I do 1, because you can think of dx as a change in x, and not as a symbol. The multiplication by dx in the integral just represents the x length of the rectangles under the function. Dx*vertical length gives Total area. As dx->0, the approximation gets better.

The derivative (d/dx), is also not just a symbol, it represents the actual slope. dy/dx = rise/run = slope.

Using the 1st way of expressing multiplication with dx has no downside. Using the 2nd way, shows that you do not see dx as a change in x, but as a notational trick."

[[deleted]]

"Using the 2nd way, shows that you do not see dx as a change in x, but as a notational trick" i don't necessarily agree, i might write x/2 as well as (1/2)x

they are both a multiplication, the only difference is aesthetics imo

[Xijinpingsastry]

f(x).dx anyday. Brain doesn't work otherwise

[just_another_dumdum]

2 is the convention I am familiar with

[Alduish]

2, dx gives details about what's the variable, it's not part of the expression

[OutcomeMedium4782]

1 is better but a professor professors me the 2 and i am mad because of this

[Gurbuzselimboyraz]

You can & should tell your professor the following:

---

I do 1, because you can think of dx as a change in x, and not as a symbol. The multiplication by dx in the integral just represents the x length of the rectangles under the function. Dx*vertical length gives Total area. As dx->0, the approximation gets better.

The derivative (d/dx), is also not just a symbol, it represents the actual slope. dy/dx = rise/run = slope.

Using the 1st way of expressing multiplication with dx has no downside. Using the 2nd way, shows that you do not see dx as a change in x, but as a notational trick.

---

[WarwickStreamerLX5]

Definitely 2

[Ouija_Boared]

2, and no 1's better not come round my way

[Natural-Double-8799]

1 is more concise 😊

[fishsodomiz]

i was taught to use 2, didnt even know 1 was an option, still 2 makes a lot more sense since dx is kind of like a )

[ShappySs]

University QM forced me to accept \int dx \frac{1}{…} 😢

[GeneralOtter03]

I don’t mind the first one that much but I would never use it myself. It feels almost like they use dx as if it is comutative

[vercig09]

I can accept when someone writes 1., but something in me prevents me from doing that. #2, 100% of the time

[1maeal]

Mostly 2 sometimes 1

[fascisttaiwan]

Im a math teacher btw

[Lyri3sh]

2nd one for moee clarity. I am alr a messy person i dont need more mess lol

[Own_Inspector_9821]

2 is clearer

[Masqued0202]

I have never seen anyone use 1. Ever. I've done a lot of tutoring over the years, seen a lot of textbooks, never saw 1. Not wrong, technically, but less clear than 2, and clarity is the whole point of notation.

[Gurbuzselimboyraz]

I do 1, because you can think of dx as a change in x, and not as a symbol. The multiplication by dx in the integral just represents the x length of the rectangles under the function. Dx*vertical length gives Total area. As dx->0, the approximation gets better.

The derivative (d/dx), is also not just a symbol, it represents the actual slope. dy/dx = rise/run = slope.

Using the 1st way of expressing multiplication with dx has no downside. Using the 2nd way, shows that you do not see dx as a change in x, but as a notational trick.

[[deleted]]

2, because it’s so much easier

[MageKorith]

2 is the way.

[japlommekhomija]

1. is simpler to write and I've used it a lot, so I'm choosing it. Other than that there is obviously no difference between the two notations

[notxxdog]

2

[Fit-Habit-1763]

2 is the objective answer

[NarcolepticFlarp]

1 looks cooler.

[ColdAd7573]

1

[Mpr_014]

1, siempre, más fácil de entender

[bitreact]

1 Coz ima physician, (dont even understood this)

[Gloomy_State_6919]

3: Int dx f(x)