Evaluate the surface integral 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) = x² i + y² j + z² k S is the boundary of the solid half-cylinder 0 s zsV 4 - - y², 0 s x s 4 64T
Evaluate the surface integral 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) = x² i + y² j + z² k S is the boundary of the solid half-cylinder 0 s zsV 4 - - y², 0 s x s 4 64T
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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not 32pi or 64pi

Transcribed Image Text:Evaluate the surface integral
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.
x2 i + y2 j + z2 k
F(x, у, 2) :
S is the boundary of the solid half-cylinder 0 < z< V 4 - y2, 0< x < 4
64n
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