For the following exercises, use a computer algebraic system (CAS) and the divergence theorem to evaluate surface integral ∫ s F ⋅ n d S for the given choice of F and the boundary surface S . For each closed surface, assume N is the outward unit normal vector. 394. Consider F ( x , y , z ) = x 2 i + x y j + ( z + 1 ) k . Let E be the solid enclosed by paraboloid z = 4 − x 2 − y 2 and plane z = 0 with normal vectors painting outside E . Compute flux F across the boundary of E using the divergence theorem.
For the following exercises, use a computer algebraic system (CAS) and the divergence theorem to evaluate surface integral ∫ s F ⋅ n d S for the given choice of F and the boundary surface S . For each closed surface, assume N is the outward unit normal vector. 394. Consider F ( x , y , z ) = x 2 i + x y j + ( z + 1 ) k . Let E be the solid enclosed by paraboloid z = 4 − x 2 − y 2 and plane z = 0 with normal vectors painting outside E . Compute flux F across the boundary of E using the divergence theorem.
For the following exercises, use a computer algebraic system (CAS) and the divergence theorem to evaluate surface integral
∫
s
F
⋅
n
d
S
for the given choice of F and the boundary surface S. For each closed surface, assume N is the outward unit normal vector.
394. Consider
F
(
x
,
y
,
z
)
=
x
2
i
+
x
y
j
+
(
z
+
1
)
k
. Let E be the solid enclosed by paraboloid
z
=
4
−
x
2
−
y
2
and plane
z
=
0
with normal vectors painting outside E. Compute flux F across the boundary of E using the divergence theorem.
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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01 - What Is an Integral in Calculus? Learn Calculus Integration and how to Solve Integrals.; Author: Math and Science;https://www.youtube.com/watch?v=BHRWArTFgTs;License: Standard YouTube License, CC-BY