Dy multiplied by y (order matters?)

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SUMMARY

The discussion centers on the integration of the equation dT=1/2 * [(m/L)dy]*[yx/L]^2, where y is the variable. Participants confirm that it is correct to rearrange the equation to ∫y^2 dy, treating dy as a differential that can be repositioned. The integral ultimately takes the form ∫k y^2 dy, with k being a constant derived from the problem's parameters. This confirms that the order of multiplication does not affect the integration process.

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az91
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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
 
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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.
 

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