# Is it possible to integrate this?

1. Jul 20, 2015

### 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?

2. Jul 20, 2015

### Staff: Mentor

3. Jul 20, 2015

### micromass

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

4. Jul 20, 2015

### 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