Selecting Techniques for Antidifferentiation
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
What is the antiderivative of
cot
(
x
)
\cot(x)
cot
(
x
)
?
QUESTION
Choose the technique for
ln
(
a
x
)
\text{ln}(a^x)
ln
(
a
x
)
.
QUESTION
What is the antiderivative of
cos
2
(
x
)
\text{cos}^2(x)
cos
2
(
x
)
?
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ANSWER
x
2
+
1
4
sin
(
2
x
)
+
C
\frac{x}{2} + \frac{1}{4}\text{sin}(2x) + C
2
x
+
4
1
sin
(
2
x
)
+
C
. Use double angle identity:
cos
2
(
x
)
=
1
+
cos
(
2
x
)
2
\text{cos}^2(x) = \frac{1 + \text{cos}(2x)}{2}
cos
2
(
x
)
=
2
1
+
cos
(
2
x
)
.
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