Integrating Using Substitution
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Identify
u
u
u
for substitution if
d
u
=
sec
2
x
d
x
du = \text{sec}^2 x \, dx
d
u
=
sec
2
x
d
x
.
QUESTION
Determine
d
u
du
d
u
if
u
=
ln
(
4
x
)
u = \text{ln}(4x)
u
=
ln
(
4
x
)
in substitution.
QUESTION
Determine
d
u
du
d
u
if
u
=
ln
x
u = \text{ln } x
u
=
ln
x
in substitution.
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ANSWER
d
u
=
1
x
d
x
du = \frac{1}{x} \, dx
d
u
=
x
1
d
x
. The derivative of
u
=
ln
x
u = \ln x
u
=
ln
x
is
1
x
\frac{1}{x}
x
1
, so
d
u
=
1
x
d
x
du = \frac{1}{x} dx
d
u
=
x
1
d
x
.
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