Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check for agreement. x² y² z² yz): 9827 +2=1} F = (z-y,x, -x); D={(x,y/2): Set up the volume integral for the Divergence Theorem. Select the correct choice below and fill in any answer boxes within your choice. O A. &B O A. !!! SSS dx dy dz, where the integrand does not simplify to a constant 000 OB. •SSO. D (Type an integer or a simplified fraction.) The integral simplifies to Set up the surface integral for the Divergence Theorem, using a parametrization with the form r= (a sin u cos v, b sinu sin v, c cos u) for the surface if needed. Select the correct choice below and fill in any answer boxes within your choice. !! 0 0 dV. du dv, where the integrand does not simplify to a constant The integral simplifies to C ds. S (Type an integer or a simplified fraction.)
Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check for agreement. x² y² z² yz): 9827 +2=1} F = (z-y,x, -x); D={(x,y/2): Set up the volume integral for the Divergence Theorem. Select the correct choice below and fill in any answer boxes within your choice. O A. &B O A. !!! SSS dx dy dz, where the integrand does not simplify to a constant 000 OB. •SSO. D (Type an integer or a simplified fraction.) The integral simplifies to Set up the surface integral for the Divergence Theorem, using a parametrization with the form r= (a sin u cos v, b sinu sin v, c cos u) for the surface if needed. Select the correct choice below and fill in any answer boxes within your choice. !! 0 0 dV. du dv, where the integrand does not simplify to a constant The integral simplifies to C ds. S (Type an integer or a simplified fraction.)
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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Transcribed Image Text:Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check for agreement.
z²
0= {(xXxx): + ² + ² + 2 = = 1}
D=
,y,z):
9
8
27
F = (z-y,X, - x);
Set up the volume integral for the Divergence Theorem. Select the correct choice below and fill in any answer boxes within your choice.
O A.
O A.
SS S dx dy dz, where the integrand does not simplify to a constant
00 0
O B.
•SSS (0) av.
D
(Type an integer or a simplified fraction.)
Set up the surface integral for the Divergence Theorem, using a parametrization with the form r = (a sin u cos v, b sin u sin v, c cos u) for the surface if needed. Select the correct choice below and fill in any
answer boxes within your choice.
The integral simplifies to
SS du dv, where the integrand does not simplify to a constant
0 0
SSO
S
(Type an integer or a simplified fraction.)
The integral simplifies to
dS
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