AP Calculus AB Quiz
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APPLICATIONS OF INTEGRATION
Question 1
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The region bounded by
x
=
1
2
y
2
x=\frac{1}{2}y^2
x
=
2
1
y
2
and the y-axis on
0
≤
y
≤
4
0\le y\le 4
0
≤
y
≤
4
is revolved about the y-axis. Which integral gives the volume?
A
π
∫
0
4
(
1
2
y
2
)
2
d
y
\pi\int_{0}^{4} \left(\frac{1}{2}y^2\right)^2\,dy
π
∫
0
4
(
2
1
y
2
)
2
d
y
B
π
∫
0
4
1
2
y
2
d
y
\pi\int_{0}^{4} \frac{1}{2}y^2\,dy
π
∫
0
4
2
1
y
2
d
y
C
π
∫
0
2
(
1
2
y
2
)
2
d
y
\pi\int_{0}^{2} \left(\frac{1}{2}y^2\right)^2\,dy
π
∫
0
2
(
2
1
y
2
)
2
d
y
D
π
∫
0
4
(
2
y
2
)
2
d
y
\pi\int_{0}^{4} \left(\frac{2}{y^2}\right)^2\,dy
π
∫
0
4
(
y
2
2
)
2
d
y
E
π
∫
0
4
(
1
2
y
2
)
2
d
x
\pi\int_{0}^{4} \left(\frac{1}{2}y^2\right)^2\,dx
π
∫
0
4
(
2
1
y
2
)
2
d
x
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