Integration used in Derivations

Question

I've seen many derivations in which Integration is used. But I don't understand the fact that why after going to a distance like $y$ or $x$, we take an element $dy$ or $dx$? Instead can't we take any other element of a different width say $dtheta$ after going to $y$?
What does this mean?

gandalf61 · Answer

If you want to integrate some attribute $f$ with respect to $theta$ - and if you think it is physically meaningful to do that - then you an certainly do so. But you will need to find an expression for $f$ as a function of $theta$. In other words $int f(theta) space d theta$ makes sense, but $int f(x) space d theta$ does not unless you know how $x$ varies with $theta$.

Answered by gandalf61 on February 17, 2021

Integration used in Derivations

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