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Mathematics
Problem
Which of the following definite integrals gives the volume of the solid obtained when the region bounded by
y
=
2
x
y=2x
y
=
2
x
, the
x
x
x
-axis, and
x
=
1
x=1
x
=
1
is revolved about the line
y
=
−
1
y=-1
y
=
−
1
? a)
π
∫
0
1
(
2
x
+
1
)
2
d
x
\pi\displaystyle\int_{0}^{1}(2x+1)^2\,dx
π
∫
0
1
(
2
x
+
1
)
2
d
x
b)
2
π
∫
0
1
x
(
2
x
+
1
)
d
x
2\pi\displaystyle\int_{0}^{1}x(2x+1)\,dx
2
π
∫
0
1
x
(
2
x
+
1
)
d
x
c)
π
∫
0
1
[
(
2
x
+
1
)
2
−
1
]
d
x
\pi\displaystyle\int_{0}^{1}\bigl[(2x+1)^2-1\bigr]\,dx
π
∫
0
1
[
(
2
x
+
1
)
2
−
1
]
d
x
d)
π
∫
0
1
(
x
+
1
)
2
d
x
\pi\displaystyle\int_{0}^{1}(x+1)^2\,dx
π
∫
0
1
(
x
+
1
)
2
d
x
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