Is it possible to integrate this?

[Abtinnn]

Let's say you have an equation like this:

dy=f(x) dx²

Would it be possible to integrate both sides of the equation?

 

[jedishrfu]

Here's a similar thread on this problem:

https://www.physicsforums.com/threads/integration-of-dx-2.622181/

 

[micromass]

Let's say you have an equation like this:

dy=f(x) dx²

Would it be possible to integrate both sides of the equation?

Yes, but the integral will always be zero. More precisely, if $f:[a,b]\rightarrow \mathbb{R}$ is continuous, then $\int_a^b f(x)dx^2 = 0$.

 

[cpsinkule]

powers of a true differential are 0. dx² really means dx∧dx which is always 0. things like arc length are usually represented by ds² and integrate to finite numbers over some interval, but arc length is not a true differential form unless you restrict yourself to the curve itself, in which case it is a 1form