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As is known, we can neglect high-order term in expression ##f(x+dx)-f(x)##. For ##y=x^2##: ##dy=2xdx+dx^2##, ##dy=2xdx##.

I read that infinitesimals have property: ##dx+dx^2=dx##

I tried to neglect high-order terms in integral sum (##dx^2## and ##4dx^2## and so on) and I obtained wrong result in the end.

Where is my mistake?

Thanks.