Area Between Curves: Functions of x
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
In which scenario is
g
(
x
)
g(x)
g
(
x
)
subtracted from
f
(
x
)
f(x)
f
(
x
)
?
QUESTION
What is the integral for area:
f
(
x
)
=
sin
(
x
)
f(x) = \text{sin}(x)
f
(
x
)
=
sin
(
x
)
,
g
(
x
)
=
0
g(x) = 0
g
(
x
)
=
0
, on
[
0
,
pi
2
]
[0, \frac{\text{pi}}{2}]
[
0
,
2
pi
]
?
QUESTION
Identify the area formula for two curves
f
(
x
)
f(x)
f
(
x
)
,
g
(
x
)
g(x)
g
(
x
)
where
f
(
x
)
≠
g
(
x
)
f(x) \neq g(x)
f
(
x
)
=
g
(
x
)
on
[
a
,
b
]
[a, b]
[
a
,
b
]
.
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ANSWER
integral from
a
to
b
of
∣
f
(
x
)
−
g
(
x
)
∣
d
x
\text{integral from } a \text{ to } b \text{ of } |f(x) - g(x)| \, dx
integral from
a
to
b
of
∣
f
(
x
)
−
g
(
x
)
∣
d
x
. Absolute value ensures positive area when curves switch positions.
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