Integration By Parts: Finding Missing Pieces in Definite Integrals

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Darren Kuropatwa

More on the technique of antidifferentiation by substitution.

Integration By Parts
looking for the missing piece ...

Fill in the blank

Substitution: The Big Idea ...

=

Resubstitute
Substitute

=
Antidifferentiate

Substitution ... when some pieces are missing ...

Substitution ... when some pieces are missing ...

Substitution ... when some pieces are missing in a
deﬁnite integral ...

Substitution ... when some pieces are missing ...

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Integration By Parts: Finding Missing Pieces in Definite Integrals

1. Integration By Parts looking for the missing piece ... Fill in the blank

2. Substitution: The Big Idea ... = Resubstitute Substitute = Antidifferentiate

3. Substitution ... when some pieces are missing ...

4. Substitution ... when some pieces are missing ...

5. Substitution ... when some pieces are missing in a deﬁnite integral ...

6. Substitution ... when some pieces are missing ...