Behavior of Accumulation Functions Involving Area
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
What is the effect of reversing the limits of integration?
QUESTION
What does a positive value for
Integral
(
a
,
b
)
f
(
x
)
d
x
\text{Integral}(a,b) f(x)dx
Integral
(
a
,
b
)
f
(
x
)
d
x
indicate?
QUESTION
Find the accumulation function
F
(
x
)
=
∫
a
x
f
(
t
)
d
t
F(x) = \int_a^x f(t) \, dt
F
(
x
)
=
∫
a
x
f
(
t
)
d
t
. What is
F
′
(
x
)
F'(x)
F
′
(
x
)
?
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ANSWER
F
′
(
x
)
=
f
(
x
)
F'(x) = f(x)
F
′
(
x
)
=
f
(
x
)
. Fundamental Theorem: derivative of accumulation function is integrand.
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