Evaluate the integral ∬ σ f x , y , z d S over the surface σ represented by the vector -valued function r u , υ . f x , y , z = x y z ; r u , υ = u cos υ i + u sin υ j + 3 u k 1 ≤ u ≤ 2 , 0 ≤ υ ≤ π / 2
Evaluate the integral ∬ σ f x , y , z d S over the surface σ represented by the vector -valued function r u , υ . f x , y , z = x y z ; r u , υ = u cos υ i + u sin υ j + 3 u k 1 ≤ u ≤ 2 , 0 ≤ υ ≤ π / 2
Evaluate the integral
∬
σ
f
x
,
y
,
z
d
S
over the surface
σ
represented by the vector-valued function
r
u
,
υ
.
f
x
,
y
,
z
=
x
y
z
;
r
u
,
υ
=
u
cos
υ
i
+
u
sin
υ
j
+
3
u
k
1
≤
u
≤
2
,
0
≤
υ
≤
π
/
2
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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