# Weird integration problem.

1. Oct 20, 2006

### 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.

2. Oct 20, 2006

### 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.

3. Oct 20, 2006

### Checkfate

Okay, thanks again.

4. Oct 20, 2006

### HallsofIvy

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

5. Oct 20, 2006

### 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.