Question

Solve surface integral ∬(?+?+?)??? where S is hemisphere ?^2+?^2+?^2=4 , ?≥0.

Answer #1

Compute the surface integral over the given oriented
surface:
F=〈0,9,x2〉F=〈0,9,x2〉 , hemisphere
x2+y2+z2=4x2+y2+z2=4, z≥0z≥0 , outward-pointing
normal

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) = yi − xj + 4zk, S is the hemisphere x^2 +
y2^ + z^2 = 4, z ≥ 0, oriented downward

Evaluate the surface integral (double integral) over S: G(x,y,z)
d sigma using a parametric description of the surface.
G(x,y,z)= 3z^2, over the hemisphere x^2+y^2+z^2=16, with z
greater than or equal to 0.

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.

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) = yi − xj + 2zk,
S is the hemisphere
x2 + y2 + z2 = 4,
z ≥ 0,
oriented downward

Compute the surface integral of F(x, y, z) = (y,z,x) over the
surface S, where S is the portion of the cone x = sqrt(y^2+z^2)
(orientation is in the negative x direction) between the planes x =
0, x = 5, and above the xy-plane.
PLEASE EXPLAIN

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) = xz i + x j + y k S is the hemisphere x2 +
y2 + z2 = 4, y ≥ 0, oriented in the direction of the positive
y-axis. Incorrect: Your answer is incorrect.

Evaluate the surface integral ∬ 4? ? ??, where ? is the portion
of the sphere ? 2 + ? 2 + ? 2 = 10 which lies above the plane ? =
1

Evaluate the surface integral.
S
x2yz dS, S is the part of the plane
z = 1 + 2x + 3y
that lies above the rectangle
[0, 4] × [0, 2]

Solve the following integrals:
1. The integral of 2 (on top) to 0 (on bottom) of dt / (the
square root of 4+t^2)
2.The integral of 3 (on top) to 2 (on bottom) of dx / (a^2+x^2)
^ 3/2 , a > 0

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