Question
In: Math
Evaluate the surface integral. Double integral x dS, S is the triangular region with vertices (1,...
Evaluate the surface integral.
Double integral x dS, S is the triangular region with vertices (1, 0, 0), (0, −2, 0), and (0, 0, 6).
Solutions
milcah answered 1 year agoRelated Solutions
Evaluate the surface integral. S x2yz dS, S is the part of the plane z =...
Evaluate the surface integral.
S
x2yz dS, S is the part of the plane
z = 1 + 2x + 3y
that lies above the rectangle
[0, 3] × [0, 2]
Evaluate the surface integral S F · dS for the given vector field F and the...
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 = 6 − x2 − y2 that lies above the square
0 ≤ x ≤ 1, 0 ≤ y ≤ 1,
and has...
Evaluate the surface integral S F · dS for the given vector field F and...
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 = 1
in the first octant, with orientation toward the origin
Evaluate the surface integral S F · dS for the given vector field F and...
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 = 9
in the first octant, with orientation toward the origin
Evaluate the surface integral S F · dS for the given vector field F and the...
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) =
xzey i −
xzey j + z
k
S is the part of the plane x + y +
z = 3 in the first octant and has downward orientation
Evaluate the surface integral S F · dS for the given vector field F and...
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 + z4 k
S is the part of the cone z =
x2 + y2
beneath the plane
z = 1
with downward orientation
1. Evaluate the double integral for the function f(x,y) and the given region R. R is...
1. Evaluate the double integral for the function
f(x,y) and the given region
R.
R is the rectangle defined by
-2 x 3 and
1 y e4
2. Evaluate the double integral
f(x, y) dA
R
for the function f(x, y) and the
region R.
f(x, y) =
y
x3 + 9
; R is bounded by the lines
x = 1, y = 0, and y = x.
3. Find the average value of the function
f(x,y) over the plane region
R....
Evaluate the following integral, ∫ ∫ S (x2 + y2 + z2) dS, where S is...
Evaluate the following integral,
∫
∫
S
(x2 + y2 + z2) dS,
where S is the part of the cylinder x2 +
y2 = 64 between the planes z = 0 and
z = 7, together with its top and bottom disks.
Use the Divergence Theorem to calculate the surface integral S F · dS; that is, calculate...
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 = 1 and the planes z = x + 8 and z = 0
Consider the function f(x, y) = 3+xy−x−2y. Let D be the closed triangular region with vertices...
Consider the function f(x, y) = 3+xy−x−2y. Let D be the closed
triangular region with vertices (1, 4), (5, 0), and (1, 0). Find
the absolute maximum and the absolute minimum of f on D.
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