Question

Find the flux of the vector field **F** =
*x* **i** +
*e*^{6x} **j** +
*z* **k** through the surface *S* given
by that portion of the plane 6*x* + *y* +
3*z* = 9 in the first octant, oriented upward.
**PLEASE EXPLAIN STEPS**. Thank you.

Answer #1

PLEASE explain STEPS. Thank you :)
Find the flux of the vector field F =
x i +
e6x j +
z k through the surface S given
by that portion of the plane 6x + y +
3z = 9 in the first octant, oriented upward. (a clear
explained answer would be appreciated)

Find the flux of the vector field F(x, y, z) = x, y, z through
the portion of the parabaloid z = 16 - x^2-y^2 above the
plane ? = 7 with upward pointing normal.

Use the divergence theorem to calculate the flux of the vector
field F = (y +xz) i+ (y + yz) j - (2x + z^2) k upward through the
first octant part of the sphere x^2 + y^2 + z^2 = a^2.

Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = x i − z j + y k
S is the part of the sphere
x2 + y2 + z2 = 4
in the first octant, with orientation toward the origin

Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = x i − z j + y k
S is the part of the sphere
x2 + y2 + z2 = 25
in the first octant, with orientation toward the origin

Evaluate the surface integral ∫∫S
F · dS for the given
vector field F and the oriented surface
S. In other words, find the flux of F
across S. For closed surfaces, use the positive (outward)
orientation.
F(x, y, z) =
x i - z j +
y k
S is the part of the sphere x2 +
y2 + z2 = 81 in the first
octant, with orientation toward the origin.

compute the flux of the vector field F through the parameterized
surface S. F= zk and S is oriented upward and given, for 0 ≤ s ≤ 1,
0 ≤ t ≤ 1, by x = s + t, y = s – t, z = s2 +
t2.
the answer should be 4/3.

Evaluate the surface integral S F · dS for the given vector
field F and the oriented surface S. In other words, find the flux
of F across S. For closed surfaces, use the positive (outward)
orientation. F(x, y, z) = y i − x j + z2 k S is the helicoid (with
upward orientation) with vector equation r(u, v) = u cos v i + u
sin v j + v k, 0 ≤ u ≤ 5, 0...

Find the flux of the vector field F (x, y, z) =< y, x, e^xz
> outward from the z−axis and across the surface S, where S is
the portion of x^2 + y^2 = 9 with x ≥ 0, y ≥ 0 and −3 ≤ z ≤ 3.

Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = xy i + yz j + zx k
S is the part of the paraboloid
z = 4 − x2 − y2 that lies above the square
0 ≤ x ≤ 1, 0 ≤ y ≤ 1,
and has...

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