I'm in a physic formation and we are used to play with the infinitesimal elements $dx$ of integration like a variable (for example the calculation of the pressure of a gas), because we look at small movements or small volume/surface before integrating and sometimes I end with strange expressions and I don't know if there is a meaning or how to make it right.
For example:
- If I have an expression like: $p(x)\ dx = A$, how can I integrate the equation without $dx$ with $A$?
- In many situations, I have things like $\dfrac{f(x)}{dx}$ or more complicated things like $f(x)*g(dx)$ with $f(x)$ and $g(x)$ are functions. How can I integrate such things?
And if someone has a good summary on authorized operations with $dx$, I am very interested!
Thank you for your answers.