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Mathematics
Problem
Region
P
P
P
is bounded by
y
=
x
y=x
y
=
x
,
y
=
0
y=0
y
=
0
, and
x
=
2
x=2
x
=
2
. Which integral represents the volume of the solid formed when
P
P
P
is revolved about the vertical line
x
=
5
x=5
x
=
5
? a)
π
∫
0
2
(
5
−
y
)
2
d
y
\displaystyle \pi\int_{0}^{2}(5-y)^{2}\,dy
π
∫
0
2
(
5
−
y
)
2
d
y
b)
π
∫
0
2
(
25
−
(
5
−
y
)
2
)
d
y
\displaystyle \pi\int_{0}^{2}\bigl(25-(5-y)^{2}\bigr)\,dy
π
∫
0
2
(
25
−
(
5
−
y
)
2
)
d
y
c)
π
∫
0
2
(
(
5
−
y
)
2
−
9
)
d
y
\displaystyle \pi\int_{0}^{2}\bigl((5-y)^{2}-9\bigr)\,dy
π
∫
0
2
(
(
5
−
y
)
2
−
9
)
d
y
d)
π
∫
0
2
(
5
−
x
)
x
d
x
\displaystyle \pi\int_{0}^{2}(5-x)x\,dx
π
∫
0
2
(
5
−
x
)
x
d
x
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