Re: Explanation of this hypothesis of SUBSTITUTION RULE requested

From: True Raptor <CB4ever@xxxxxxxxxxxxxxx>
Date: Sun, 19 Feb 2006 20:01:00 -0500

deniz.bahar@xxxxxxxxx wrote:

My question deals with this following RULE/THEOREM:

The Substitution Rule: If u=g(x) is a differentiable function whose
range is an inteval on which f is continuous, then

integral[ f (g(x)) g' (x) ] = integral[ f (u) du ]

I can't understand why the condition "whose range is an interval on
which f is continuous" is needed. What are some cases that could
break this, and not allow us to use substitution (yet look on the
surface as a good place to use substit.) ?

%%%%%%%%%%
D. Bahar

If g is defined for some values for which f is not continuous, then the integral does not exist. Integration requires continuity.

CB4Ever
.

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