Question

F(x, y, z) =< 3xy^2 , xe^z , z^3 >, S is the solid bounded
by the cylinder y^{2} + z^{2} = 1 and the planes x
= −1 and x = 2 Find he surface area using surface integrals. DO NOT
USE Divergence Theorem. Answer: 9π/2

Answer #1

Any doubt in this then comment below..

For surface area , we ficus on 3 surface...top , bottom , and curved part ...

F(x, y, z) = xye^zˆi + xy^2 z^3ˆj − ye^zˆk,S is the surface of
the box bounded by the coordinate planes and the planes x = 3, y =
2, and z = 1. Find the surface area using surface integrals. DO NOT
use divergence theorem.

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.

Verify the Divergence Theorem for the vector field F(x, y, z) =
< y, x , z^2 > on the region E bounded by the planes y + z =
2, z = 0 and the cylinder x^2 + y^2 = 1.
By Surface Integral:
By Triple Integral:

Problem Verify the Divergence
Theorem for the vector fifield
F(x, y, z) = <y, x,
z^2>on the region E bounded by the planes
y + z = 2,
z = 0 and the cylinder x^2 + y^2 =
1.
1.Surface Integral:
2.Triple Integral:

Find the volume of the solid bounded by the cylinder x^2+y^2=9
and the planes z=-10 and 1=2x+3y-z

Let D be the solid in the first octant bounded by the planes
z=0,y=0, and y=x and the cylinder 4x2+z2=4.
Write the triple integral in all 6 ways.

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

Q8. Let G be the cylindrical solid bounded by x2 + y2 = 9, the
xy-plane, and the plane
∫∫
z = 2, and let S be its surface. Use the Divergence Theorem to
evaluate I = S F · ndS where F(x,y,z) = x3i + y3j + z3k and n is
the outer outward unit normal to S.

draw the solid bounded above z=9/2-x2-y2
and bounded below x+y+z=1. Find the volume of this
solid.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 33 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago