AP Calculus AB Quiz
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APPLICATIONS OF INTEGRATION
Question 1
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Region bounded by
y
=
e
−
x
y=e^{-x}
y
=
e
−
x
and
y
=
0
y=0
y
=
0
for
0
≤
x
≤
1
0\le x\le1
0
≤
x
≤
1
is revolved about
y
=
2
y=2
y
=
2
. Which setup is correct?
A
V
=
π
∫
0
1
[
(
2
−
e
−
x
)
2
−
(
2
−
0
)
2
]
d
x
V=\pi\int_{0}^{1}\big[(2-e^{-x})^2-(2-0)^2\big]dx
V
=
π
∫
0
1
[
(
2
−
e
−
x
)
2
−
(
2
−
0
)
2
]
d
x
B
V
=
π
∫
0
1
[
(
2
−
0
)
2
−
(
2
−
e
−
x
)
2
]
d
x
V=\pi\int_{0}^{1}\big[(2-0)^2-(2-e^{-x})^2\big]dx
V
=
π
∫
0
1
[
(
2
−
0
)
2
−
(
2
−
e
−
x
)
2
]
d
x
C
V
=
π
∫
0
1
[
(
e
−
x
)
2
−
0
2
]
d
x
V=\pi\int_{0}^{1}\big[(e^{-x})^2-0^2\big]dx
V
=
π
∫
0
1
[
(
e
−
x
)
2
−
0
2
]
d
x
D
V
=
π
∫
0
1
[
(
e
−
x
−
2
)
2
−
(
0
−
2
)
2
]
d
x
V=\pi\int_{0}^{1}\big[(e^{-x}-2)^2-(0-2)^2\big]dx
V
=
π
∫
0
1
[
(
e
−
x
−
2
)
2
−
(
0
−
2
)
2
]
d
x
E
V
=
π
∫
0
1
[
(
2
−
e
−
x
)
−
(
2
−
0
)
]
2
d
x
V=\pi\int_{0}^{1}\big[(2-e^{-x})-(2-0)\big]^2dx
V
=
π
∫
0
1
[
(
2
−
e
−
x
)
−
(
2
−
0
)
]
2
d
x
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