Solving an Integral with a Twist - How to Approach it?

[Apteronotus]

How can the following integral be approached?
$$\int f(t) \sqrt{dt}$$

thanks in advance.

 

[Ben Niehoff]

I'm pretty sure it's meaningless. The units don't work out.

However, it would make sense to write something like

$$\int_C f(x,y) \sqrt{dx^2 + dy^2}$$

where C is some contour.

 

[g_edgar]

There was a long argument about this in one of the forums a few months ago. But Apteronotus will have to give us a context before we can say anything about it.

 

[lugita15]

It doesn't make sense. Since $$\sqrt{x+dx} = \sqrt{x} + \frac{dx}{2\sqrt{x}}$$, it follows that $$\sqrt{dx} = dx/0$$, which is of course meaningless.

 

[lugita15]

There was a long argument about this in one of the forums a few months ago. But Apteronotus will have to give us a context before we can say anything about it.

Do you have a link to this thread? I'd be interested in reading it.