Multivariable Calculus Quiz
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INTEGRAL THEOREMS
Question 1
of 14
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Let
C
C
C
be the triangular path from
(
1
,
0
,
0
)
(1,0,0)
(
1
,
0
,
0
)
to
(
0
,
1
,
0
)
(0,1,0)
(
0
,
1
,
0
)
to
(
0
,
0
,
1
)
(0,0,1)
(
0
,
0
,
1
)
and back to
(
1
,
0
,
0
)
(1,0,0)
(
1
,
0
,
0
)
. Let
F
⃗
(
x
,
y
,
z
)
=
⟨
z
2
,
x
2
,
y
2
⟩
\vec{F}(x,y,z) = \langle z^2, x^2, y^2 \rangle
F
(
x
,
y
,
z
)
=
⟨
z
2
,
x
2
,
y
2
⟩
. Evaluate
∮
C
F
⃗
⋅
d
r
⃗
\oint_C \vec{F} \cdot d\vec{r}
∮
C
F
⋅
d
r
.
A
−
1
-1
−
1
B
1
1
1
C
1
/
3
1/3
1/3
D
2
/
3
2/3
2/3
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