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Is it possible to integrate this?

  1. Jul 20, 2015 #1
    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. jcsd
  3. Jul 20, 2015 #2


    Staff: Mentor

  4. Jul 20, 2015 #3
    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##.
  5. Jul 20, 2015 #4
    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
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