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**What is ∫ (dy)^2 ?**

__Fact:__

Let a<b.

b

∫ (dy)

^{2}= 0

a

=====================

1) First of all, I'm having trouble understanding the

*meaning*of the above integral. I tried searching my elementary calculus textbooks, but I really couldn't find ANY integral like this. I have only seen integrals like ∫ (dy) in my calculus books and so I have no idea how they can have (dy)

^{2}which makes no sense to me...

2) Why is the above fact true? How can we rigorously

*prove*it?

Hopefully someone can clarify this.

Thank you!

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