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Mathematics
Problem
The region bounded by
y
=
x
2
y = x^{2}
y
=
x
2
and
y
=
4
y = 4
y
=
4
is revolved about the
x
x
x
–axis. Which of the following definite integrals represents the volume of the resulting solid? a)
V
=
π
∫
−
2
2
(
16
−
x
4
)
d
x
V=\pi\displaystyle\int_{-2}^{2}\left(16-x^{4}\right)\,dx
V
=
π
∫
−
2
2
(
16
−
x
4
)
d
x
b)
V
=
π
∫
0
2
(
16
−
x
4
)
d
x
V=\pi\displaystyle\int_{0}^{2}\left(16-x^{4}\right)\,dx
V
=
π
∫
0
2
(
16
−
x
4
)
d
x
c)
V
=
π
∫
−
2
2
(
4
−
x
2
)
d
x
V=\pi\displaystyle\int_{-2}^{2}\left(4-x^{2}\right)\,dx
V
=
π
∫
−
2
2
(
4
−
x
2
)
d
x
d)
V
=
2
π
∫
0
4
(
4
−
x
2
)
d
x
V=2\pi\displaystyle\int_{0}^{4}\left(4-x^{2}\right)\,dx
V
=
2
π
∫
0
4
(
4
−
x
2
)
d
x
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