Linked Questions

5
votes
6answers
36k views

What does the dx mean in an integral? [duplicate]

I know dy/dx for example means "derivative of y with respect to x," but there's another context that confuses me. You will generally just see a dx term sitting at the end of an integral equation and I ...
0
votes
3answers
459 views

Can you integrate without a $dx$ [duplicate]

Long ago I realized that manipulation of derivatives was possible using algebraic quantities. One could take a differential instead of derivatives $$ d[\sin x]=\cos x\ dx $$ $$ \frac{d[\sin x]}{dx}=\...
2
votes
3answers
285 views

Does $f(x)\,dx$ denote multiplication of $f(x)$ by $dx$? [duplicate]

In the integral form $\int \! f(x) \, \mathrm{d}x$ does $f(x)\,\mathrm{d}x$ can be seen as a multiplication of $f(x)$ and $\mathrm{d}x$?
2
votes
3answers
239 views

What is $dx$ on an integral? [duplicate]

I've heard from some of my teachers it's a bilineal form and some other stuff, nobody actually ever explained me the reason of it. Of course i've done practical problems in which $dx$ is a "very small ...
0
votes
1answer
179 views

What is the meaning of $dx$? [duplicate]

What the meaning of $dx$? Does it refer to something known as a differential (whats that?). Why is it used in integration when we put: $$\int f(x) dx$$ Does it refer to the derivative of something? ...
1
vote
2answers
79 views

Why indefinite integral has such a notation? [duplicate]

Why indefinite integral has such a notation ? What part "dx" has to do with the indefinite integral, and why f(x) is multiplied by it ?
2
votes
1answer
114 views

dy/dx … what are we really saying? What is 'dx'? [duplicate]

In Professor Leonard's lectures: https://www.youtube.com/watch?v=aiBD9aI69C8&list=PLF797E961509B4EB5&index=25 ... we are starting to integrate. He keeps using 'dx', our old friend from 'dy/...
0
votes
2answers
92 views

Can $\mathrm{d}x$ be thought of as a derivative and differentiation or it's just a small change in $x$ and nothing more? [duplicate]

The $\mathrm{d}x$ appears on integrals. I saw conflicting views regarding it. People sometimes write it does have a connection to differentiation and derivatives. Does it or does it not?
0
votes
1answer
86 views

Anti derivative notation [duplicate]

$F$ is an anti derivative of $f$. $$\int f(x) dx = F(x)+C$$ Can you tell me why there is '$dx$' in the LHS?
1
vote
0answers
59 views

Clarification of meaning of dx in an integral [duplicate]

I would like to have some clarification on the physical meaning of $dx$. I already know the following in the context of the area under the curve: $\lim_{\Delta x \rightarrow 0} \sum f(x) \Delta x \...
0
votes
1answer
50 views

trouble understanding some parts of integration, [duplicate]

what does $dx$ mean in: $$\int f(x)dx$$ and is it true that, if $\frac{df(x)}{dx} = g(x)$, then: $$\int g(x)dx = \int df(x)$$
1138
votes
23answers
114k views

Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio?

In the book Thomas's Calculus (11th edition) it is mentioned (Section 3.8 pg 225) that the derivative $dy/dx$ is not a ratio. Couldn't it be interpreted as a ratio, because according to the formula $...
67
votes
10answers
12k views

Why can't the second fundamental theorem of calculus be proved in just two lines?

The second fundamental theorem of calculus states that if $f$ is continuous on $[a,b]$ and if $F$ is an antiderivative of $f$ on the same interval, then: $$\int_a^b f(x) dx= F(b)-F(a).$$ The proof of ...
48
votes
7answers
21k views

What does $dx$ mean?

$dx$ appears in differential equations, such us derivatives and integrals. For example, a function $f(x)$ its first derivative is $\dfrac{d}{dx}f(x)$ and its integral $\displaystyle\int f(x)dx$. But ...
51
votes
9answers
4k views

Is $dx\,dy$ really a multiplication of $dx$ and $dy$?

On the answers of the question Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio? it was told that $\frac{dy}{dx}$ cannot be seen as a quotient, even though it looks like a fraction. My question is: ...

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