For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 350. Use Stokes’ theorem and let C be the boundary of surface z = x 2 + y 2 with 0 ≤ x ≤ 2 and 0 ≤ y ≤ 1 , oriented with upward facing normal. Define F ( x , y , z ) = [ sin ( x 3 ) + x z ] i + ( x − y z ) j + cos ( z 4 ) k and evaluate ∫ c F ⋅ d S .
For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 350. Use Stokes’ theorem and let C be the boundary of surface z = x 2 + y 2 with 0 ≤ x ≤ 2 and 0 ≤ y ≤ 1 , oriented with upward facing normal. Define F ( x , y , z ) = [ sin ( x 3 ) + x z ] i + ( x − y z ) j + cos ( z 4 ) k and evaluate ∫ c F ⋅ d S .
For the following exercises, use Stokes’ theorem to evaluate
∬
s
(
c
u
r
l
F
⋅
N
)
d
S
for the vector fields and surface.
350. Use Stokes’ theorem and let C be the boundary of surface
z
=
x
2
+
y
2
with
0
≤
x
≤
2
and
0
≤
y
≤
1
, oriented with upward facing normal. Define
F
(
x
,
y
,
z
)
=
[
sin
(
x
3
)
+
x
z
]
i
+
(
x
−
y
z
)
j
+
cos
(
z
4
)
k
and evaluate
∫
c
F
⋅
d
S
.
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.
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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