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Mathematics
Mathematics
Problem
The region enclosed by
y
=
∣
x
∣
y=|x|
y
=
∣
x
∣
and
y
=
x
2
y=x^{2}
y
=
x
2
for
−
1
≤
x
≤
1
-1\le x\le 1
−
1
≤
x
≤
1
is revolved about the
x
x
x
-axis. Which of the following expressions represents the exact volume of the resulting solid? a)
π
∫
−
1
1
(
∣
x
∣
−
x
2
)
d
x
\pi\displaystyle\int_{-1}^{1}\bigl(|x|-x^{2}\bigr)\,dx
π
∫
−
1
1
(
∣
x
∣
−
x
2
)
d
x
b)
π
[
2
∫
0
1
(
x
4
−
x
2
)
d
x
]
\pi\left[2\displaystyle\int_{0}^{1}\bigl(x^{4}-x^{2}\bigr)\,dx\right]
π
[
2
∫
0
1
(
x
4
−
x
2
)
d
x
]
c)
π
[
2
∫
0
1
(
x
2
−
x
4
)
d
x
]
\pi\left[2\displaystyle\int_{0}^{1}\bigl(x^{2}-x^{4}\bigr)\,dx\right]
π
[
2
∫
0
1
(
x
2
−
x
4
)
d
x
]
d)
π
[
2
∫
0
1
(
x
−
x
2
)
2
d
x
]
\pi\left[2\displaystyle\int_{0}^{1}\bigl(x-x^{2}\bigr)^{2}\,dx\right]
π
[
2
∫
0
1
(
x
−
x
2
)
2
d
x
]
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