Use the Divergence Theorem to find the flux of F across the surface σ with outward orientation. F x , y , z = x 2 + y i + z 2 j + e y − z k ; σ is the surface of the rectangular solid bounded by the coordinate planes and the planes x = 3 , y = 1 , and z = 2 .
Use the Divergence Theorem to find the flux of F across the surface σ with outward orientation. F x , y , z = x 2 + y i + z 2 j + e y − z k ; σ is the surface of the rectangular solid bounded by the coordinate planes and the planes x = 3 , y = 1 , and z = 2 .
Use the Divergence Theorem to find the flux of F across the surface
σ
with outward orientation.
F
x
,
y
,
z
=
x
2
+
y
i
+
z
2
j
+
e
y
−
z
k
;
σ
is the surface of the rectangular solid bounded by the coordinate planes and the planes
x
=
3
,
y
=
1
,
and
z
=
2
.
Determine the flux of F(x, y, z) = < −x2 + x, y, 8x3 − z + 9 > across the surface with an upward orientation. Let the surface be the portion of the paraboloid z = 9 − 4x2 −4y2 on the first octant above the plane z = 1.
Find a vector function that represents the curve of intersection of the two surfaces. The paraboloid z = 8x
2
+ y
and the parabolic cylinder y
2x
2
r(t) = ti +
j +
k
Use the Divergence Theorem to find the flux of
F(x, y, z)=z³ i-x³j+y³ k
across the sphere x² + y² + z² = a² with outward orientation.
$ = i
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