Let F be the vector field F(x, y, z) = ye"yz i+ z?xe*+» j + z( ) x+y+2 (-y+1 k defined on R'. || Let S be the part of the plane z = 3 inside the cylinders x + y = 1, x – y = 1, x + y = -1, and x – y = -1. Evaluate the surface integral , F. dS. S The surface S is oriented upward.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let F be the vector field
x-y+1
F(x, y, z) = ye*yz i + z²xe*+y j + z(-
x+y+2
k defined on R.
Let S be the part of the plane z = 3 inside the cylinders x + y = 1, x – y = 1,
x + y = -1, and x – y = -1. Evaluate the surface integral , F · dS.
The surface S is oriented upward.
Transcribed Image Text:Let F be the vector field x-y+1 F(x, y, z) = ye*yz i + z²xe*+y j + z(- x+y+2 k defined on R. Let S be the part of the plane z = 3 inside the cylinders x + y = 1, x – y = 1, x + y = -1, and x – y = -1. Evaluate the surface integral , F · dS. The surface S is oriented upward.
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