Multivariable Calculus Quiz
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SURFACE INTEGRALS
Question 1
of 10
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The surface
S
S
S
is the portion of the cone
z
=
x
2
+
y
2
z = \sqrt{x^2 + y^2}
z
=
x
2
+
y
2
between the planes
z
=
1
z = 1
z
=
1
and
z
=
3
z = 3
z
=
3
. For the scalar field
w
(
x
,
y
,
z
)
=
1
z
w(x,y,z) = \frac{1}{z}
w
(
x
,
y
,
z
)
=
z
1
, the value of
∬
S
w
d
S
\iint_S w \, dS
∬
S
w
d
S
is:
A
4
π
4\pi
4
π
B
2
π
2
2\pi\sqrt{2}
2
π
2
C
4
π
2
4\pi\sqrt{2}
4
π
2
D
8
π
8\pi
8
π
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