Use the Divergence Theorem to evaluate the flux F(x, y, z) = Consider the shown work. div(F) S F. ds. (x³,0, 2³), S is the boundary given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0 d = • (x²) + (0) + (2²³) = 3 (x² + 2²) dx дz 1 [[F. ds = ₁³ (x² + 2²) dv = [' ' ' 3 (x² + 2²) dx dydz D 3 dV W
Use the Divergence Theorem to evaluate the flux F(x, y, z) = Consider the shown work. div(F) S F. ds. (x³,0, 2³), S is the boundary given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0 d = • (x²) + (0) + (2²³) = 3 (x² + 2²) dx дz 1 [[F. ds = ₁³ (x² + 2²) dv = [' ' ' 3 (x² + 2²) dx dydz D 3 dV W
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Use the Divergence Theorem to evaluate the flux
Consider the shown work.
F(x, y, z) = (x³, 0, z³), S is the boundary given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0
Us
div(F) =
The shown work is
ə
Ə
(x²¹) + (0) + (2²) = 3 (x² + 2²)
dx
дz
1
[[¸ F · ds = [], ³ (x² + 2²) av = [ "' "' [² 3 (x² + 2²) dx dy dz
F.
3
W
Complete the statement regarding if the shown work is correct.
(Express
IS₁
S
not correct
because
only the bounds needs to be changed
✓ only the bounds needs to be changed
div(F) needs to be corrected
no changes should be made
only the integrand needs to be changed
spherical coordinates should be used
mumours in cautt form. The Symon
F. ds.
(
the bounds are not correct, but the integrand is correct
S
F. ds.
y given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0
notation and fractions where needed.)
Therefore,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f133c63-1716-41d7-8ec5-0f87428512d1%2F8405807c-1153-4ffb-96ed-a08f22df2ade%2Fqsqbswm_processed.png&w=3840&q=75)
Transcribed Image Text:Use the Divergence Theorem to evaluate the flux
Consider the shown work.
F(x, y, z) = (x³, 0, z³), S is the boundary given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0
Us
div(F) =
The shown work is
ə
Ə
(x²¹) + (0) + (2²) = 3 (x² + 2²)
dx
дz
1
[[¸ F · ds = [], ³ (x² + 2²) av = [ "' "' [² 3 (x² + 2²) dx dy dz
F.
3
W
Complete the statement regarding if the shown work is correct.
(Express
IS₁
S
not correct
because
only the bounds needs to be changed
✓ only the bounds needs to be changed
div(F) needs to be corrected
no changes should be made
only the integrand needs to be changed
spherical coordinates should be used
mumours in cautt form. The Symon
F. ds.
(
the bounds are not correct, but the integrand is correct
S
F. ds.
y given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0
notation and fractions where needed.)
Therefore,
Transcribed Image Text:Use the Divergence Theorem to evaluate the flux
F(x, y, z) = (x³, 0, z³), S is the boundary given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
Is
F. ds.
F. ds =
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