Talk:Calculus/Integration techniques/Recognizing Derivatives and the Substitution Rule

Merge with Calculus/Definite integral
This is not an integration "technique". These are basic rules that any one who does calculus should know. And, it is already in the book under Calculus/Definite integral, which is its proper place. So, I think this section should be merged into that one. NumberTheorist (talk) 04:03, 27 February 2010 (UTC)

Suggested Change 2/16/11:

If this section doesn't get merged or superseded, under "Proof of the substitution rule I would change "Let F be an anti derivative of f so F'(x) = f(x)" to Let F be an antiderivative of so F'(u) = f(u), where u = u(x). The reason being on the third line of the proof the term in the chain rule after the equal sign F'(u(x)) gets substituted for with f(u(x)).  These derivatives are with respect to u not x.


 * I cleaned up the proof of the substitution rule. I didn't implement the suggestions above because, for the first suggestion, $$x$$ is a dummy variable, so it doesn't matter what you call it; and for the second, because derivatives are being taken with respect to both $$u$$ and $$x$$.  I changed to Leibniz notation to make the application of the chain rule clearer.  I hope this addresses the issues raised, but if not, please feel free to make another comment.  I'm by no means an expert.  --Greenbreen (discuss • contribs) 18:48, 11 June 2011 (UTC)