What is the meaning of dx in integral notation?

[Checkfate]

Here I am, asking yet another question. :), Gotta keep you guys busy you know.

I am just practicing a bunch of integration questions found in a textbook a friend lent me, and I probably don't need to know how to integrate this, but I am interested anyways :).

\int_{0}^{0.5}\frac{dx}{\sqrt{1-x^{2}}}

This looks like a "Do you understand the notation", type question to me. I don't need help integrating, but only finding an antiderivative, I think I can handle the rest.

Is this some fancy way of writing \int_{0}^{0.5}\frac{1}{\sqrt{1-x^2}}dx? As this would normally be the way I would expect to see it. Or is it different? If it's what I think it is then of course the antiderivative is simply sin^{-1}x , but I want to make sure. It's an even numbered question so there is no answer in the back :(.

Thanks yet again.

 

[arildno]

Yes, it means the same thing, just imagine "dx" as a number (even if it isn't, really). Then that new way of writing "follows" (even if it doesn't, really).

conclusion:
Just another notational convenience.

 

[Checkfate]

Okay, thanks again.

 

[HallsofIvy]

You do understand, do you not, that you are asking if \frac{a}{b} is a "fancy" way of writing \frac{1}{b}a?

 

[Checkfate]

Well, I don't understand dx as being a "number" or a "unit" or anything like that in the case of integral notation. I figured that it meant that, but was not 100% sure. I could have assumed that common sense applies, but I could have been wrong right? I think that it's better to check then to assume, esspecially when learning new mathematical notation.