Dy multiplied by y (order matters?)

[az91]

Hey all, this is my first post here,

I have a question that is kind of annoying me: I came across this equation:

dT=1/2 * [(m/L)dy]*[yx/L]^2. Only y is a variable here

I need to integrate it, but my question is do I change the location of the dy and solve it as: ∫y^2 dy? I believe that this is what is done in the book but I am not sure if this is correct.

Any help will be appreciated. :D

 

[Erland]

Yes, it becomes an integral of the form $\int k\,y^2\,dy$ for some constant $k$, calculated from the parameters in the problem. $dy$ is considered as a differential and its location can be changed without problem.