Question

Use Divergence theorem to evaluate surface integral S F ·n dA where S is the surface of the solid enclosed by the tetrahedron formed by the coordinate planes x = 0, y = 0 and z = 0 and the plane 2x + 2y + z = 6 and F = 2x i − x^2 j + (z − 2x + 2y) k.

Answer #1

Use the Divergence Theorem to evaluate
S
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) =
x2i +
xyj +
zk
Q: solid region bounded by the coordinate
planes and the plane 3x + 5y +
6z = 30

Use the Divergence Theorem to evaluate
S
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) =
x2i +
xyj +
zk
Q: solid region bounded by the coordinate
planes and the plane 3x + 4y +
6z = 24

Use the Divergence Theorem to calculate the flux of ?F across
?S, where ?=??+??+??? F=zi+yj+zxk and ?S is the surface
of the tetrahedron enclosed by the coordinate planes and the
plane
?4+?4+?5=1

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) = ey
tan(z)i + y
3 − x2
j + x sin(y)k,
S is the surface of the solid that lies above the
xy-plane and below the surface
z = 2 − x4 − y4,
−1 ≤ x ≤ 1,
−1 ≤ y ≤ 1.

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.

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) =
exsin(y) i + excos(y) j + yz2k, S is the surface of the box bounded
by the planes x = 0, x = 3, y = 0, y = 1,

Use Stokes' Theorem to
evaluate the surface integral
∬ G curl F ⋅ n d S
where F ( x , y , z )
= ( z 2 − y ) i + ( x + y z ) j + x z k , G is the surface
G = { ( x , y , z ) |
z = 1 − x 2 − y 2 , z ≥ 0 }
and n
is the upward...

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 =...

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

Use Stokes' Theorem to evaluate ∫ C F · dr where F = (x +
5z) i + (3x + y) j + (4y − z) k and C is the curve of
intersection of the plane x + 2y + z = 16 with the coordinate
planes

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 13 minutes ago

asked 13 minutes ago

asked 34 minutes ago

asked 35 minutes ago

asked 44 minutes ago

asked 45 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago