Question

Evaluate the flux, ∬SF⋅dS , of F(x,y,z)=yzj+z^2k through the surface of the cylinder y^2+z^2=9 , z ≥ 0 , between the planes x=0 and x=3.

Answer #1

Evaluate the surface integral (x+y+z)dS when S is part of the
half-cylinder x^2 +z^2=1, z≥0, that lies between the planes y=0 and
y=2

Evaluate the surface integral
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 + y j + 9 k
S is the boundary of the region enclosed by the
cylinder
x2 + z2 = 1
and the planes
y = 0 and x + y =...

Evaluate the surface integral.
S
z +
x2y
dS
S is the part of the cylinder
y2 +
z2 = 4
that lies between the planes
x = 0 and x = 3
in the first octant

Use the Divergence Theorem to evaluate
F.N dS
and find the outward flux of F through the surface of the
solid bounded by the graphs of the equations.
F(x, y, z) = xi + xyj + zk
Q: solid region bounded by the coordinate planes and the plane
3x + 4y + z = 24

Evaluate the outward flux ∫∫S(F·n)dS of the vector
fieldF=yz(x^2+y^2)i−xz(x^2+y^2)j+z^2(x^2+y^2)k, where S is the
surface of the region bounded by the hyperboloid x^2+y^2−z^2= 1,
and the planes z=−1 and z= 2.

Evaluate the flux of F = 〈x^2, y^2, z^2〉 across S, where S is
portion of the cone z = √x2 + y2 between the planes z = 0 and z =
3.

Use the Divergence Theorem to calculate the surface integral
S
F · dS;
that is, calculate the flux of F across
S.
F(x, y,
z) =
x4i −
x3z2j
+
4xy2zk,
S is the surface of the solid bounded by the cylinder
x2 +
y2 = 9
and the planes
z = x + 4 and
z = 0.

The flux of
F=x^2i+y^2j+z^2k
outward across the boundary of the ball
(x−2)^2+y^2+(z−3)^2≤9
is:

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) = −xi − yj + z3k,
S is the part of the cone z =
x2 + y2
between the planes
z = 1
and
z = 2
with downward orientation

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) = x2 i + y2 j + z2 k S is the boundary of
the solid half-cylinder 0 ≤ z ≤ 25 − y2 , 0 ≤ x ≤ 3

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