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The Substitution Rule
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The Substitution Rule for Definite Integrals
Proposition
2
.
3
.
5
(Substitution Rule for Definite Integrals)
We have
assuming that
is a function that is differentiable and whose range is an interval on which
is continuous.
Proof
. If
, then by the chain rule,
is an antiderivative of
. Thus
Example
2
.
3
.
6
We let
, so
and
and the integral becomes
William Stein 2006-03-15