In my analysis textbook, the 'integration by change of variable' theorem reads(adsbygoogle = window.adsbygoogle || []).push({});

"Theorem: Consider f a continuous fonction on [a,b], g a continuous function on [c,d] such that g' is continuous on [c,d]. If g([c,d]) is a subset of [a,b] and if g(c) = a and g(d) = b, then

[tex]\int_a^b f(x)dx = \int_c^d f(g(t))g'(t)dt[/tex]

But reading the proof, I nowhere see the need for g([c,d]) being a subset of [a,b]. Is this really necessary? As long as g(c) = a and g(d) = b, it should be alright, no?

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# The 'integration by change of variable' theorem

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