3. State the Divergence Theorem (Gauss's Theorem). Let F = xz?i +(y3 + z3)j + (x² z – y²)k Use the divergence theorem to find %3D JJ, F dS where S is the hemisphere x² + y2 + z² = 4, z2 0, oriented upwards. (Use D = {(x, y, z): x2 + y2 + z² < 4, z 2 0} and aD = SUE where {(x, y, z): x2 + y? < 4, z = 0}. (Perhaps you can use: %3D %3D %3D -2m E = sin2²tdt = n)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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3. State the Divergence Theorem (Gauss's Theorem).
Let
F = xz²i +÷(y³ + z³)j + (x² z – y²)k Use the divergence theorem to find
%3D
I, F dS where S is the hemisphere x2 + y2 + z² = 4, z 2 0, oriented upwards.
(Use D = {(x,y, z): x² + y² +z² < 4, z 2 0} and aD = SUE where
E = {(x,y, z): x² + y2 < 4, z = 0}. (Perhaps you can use: sin?tdt = n)
%3D
%3D
%3D
Transcribed Image Text:3. State the Divergence Theorem (Gauss's Theorem). Let F = xz²i +÷(y³ + z³)j + (x² z – y²)k Use the divergence theorem to find %3D I, F dS where S is the hemisphere x2 + y2 + z² = 4, z 2 0, oriented upwards. (Use D = {(x,y, z): x² + y² +z² < 4, z 2 0} and aD = SUE where E = {(x,y, z): x² + y2 < 4, z = 0}. (Perhaps you can use: sin?tdt = n) %3D %3D %3D
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