- #1
sgupta31
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Homework Statement
Let D be the region x^2 + y^2 + z^2 <=4a^2, x^2 + y^2 >= a^2, and S its boundary (with
outward orientation) which consists of the cylindrical part S1 and the spherical part
S2. Evaluate the
ux of F = (x + yz) i + (y - xz) j + (z -((e^x) sin y)) k through
(a) the whole surface S using the Divergence Theorem,
(b) the surface S1 by calculating the flux integral directly,
(c) the surface S2 by calculating the flux integral directly.
Homework Equations
x^2 + y^2 + z^2 <=4a^2, x^2 + y^2 >= a^2
F = (x + yz) i + (y - xz) j + (z -((e^x) sin y))
The Attempt at a Solution
I see this to be a figure where the cylinder (radius a) is in the sphere (radius 2a).
a^2 + z^2= 4a^2
z= sqrt(3) *a
0<z<sqrt(3)*a
a<r<2a
0<theta<2*pi
I am not sure if I am doing it the right way, please point to the right direction!
Integrating wt z r theta, I get 9*sqrt(3)* (a^3)* pi for a)