For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 346. Use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S , where F ( x , y , z ) = x i + y 2 j + z e x y k and S is the part of surface z = 1 − x 2 − 2 y 2 with z ≥ 0 , oriented counterclockwise.
For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 346. Use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S , where F ( x , y , z ) = x i + y 2 j + z e x y k and S is the part of surface z = 1 − x 2 − 2 y 2 with z ≥ 0 , oriented counterclockwise.
For the following exercises, use Stokes’ theorem to evaluate
∬
s
(
c
u
r
l
F
⋅
N
)
d
S
for the vector fields and surface.
346. Use Stokes’ theorem to evaluate
∬
s
(
c
u
r
l
F
⋅
N
)
d
S
, where
F
(
x
,
y
,
z
)
=
x
i
+
y
2
j
+
z
e
x
y
k
and S is the part of surface
z
=
1
−
x
2
−
2
y
2
with
z
≥
0
, oriented counterclockwise.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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