Behavior of Accumulation Functions Involving Area
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Determine
A
′
(
x
)
A'(x)
A
′
(
x
)
if
A
(
x
)
=
integral of cos
(
t
)
from
0
to
x
A(x) = \text{integral of } \text{cos}(t) \text{ from } 0 \text{ to } x
A
(
x
)
=
integral of
cos
(
t
)
from
0
to
x
.
QUESTION
Identify the value of
A
(
x
)
A(x)
A
(
x
)
when
f
(
x
)
f(x)
f
(
x
)
is constant on
[
a
,
b
]
[a, b]
[
a
,
b
]
.
QUESTION
Determine
A
′
(
x
)
A'(x)
A
′
(
x
)
if
A
(
x
)
=
integral of
1
t
from
1
to
x
A(x) = \text{integral of } \frac{1}{t} \text{ from } 1 \text{ to } x
A
(
x
)
=
integral of
t
1
from
1
to
x
.
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ANSWER
A
′
(
x
)
=
1
x
A'(x) = \frac{1}{x}
A
′
(
x
)
=
x
1
. The derivative equals the integrand
1
x
\frac{1}{x}
x
1
by FTC.
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