Talk:Integration by Substitution/Definite Integral

In the theorem statement, should the symbol $t$ in the left-hand side integrand be replaced with $x$ to match the statement "where $x = \phi(u)$"? Also, for the substitution to be valid, shouldn't we also impose that $\phi$ be bijective? (Otherwise we might be "summing" over the same values of $x$ "multiple times" in the right hand side, right?) --Plammens (talk) 19:10, 1 March 2021 (UTC)


 * Good call on $x \to t$, changed as appropriate as needed.


 * Not sure I'm onside as regards $\phi$ being a bijection. Nothing in any of the sources I have saying anything about that. Care to check your own sources? Or find a counterexample? --prime mover (talk) 20:30, 1 March 2021 (UTC)