# Integral with a twist

## Main Question or Discussion Point

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

Ben Niehoff
Gold Member
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.

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.

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.

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.