Let W be the three dimensional region under the graph of f(x, y) = exp[-2(x² + y)] and over the region in the plane z = 0 defined by 2 < x? + y < 5. (a) Use the divergence theorem to calculate the flux of F = (x y +2 x) i+ yj-yzk out of the region W. (b) Find the flux of F out of the part of the boundary of W for which z > 0, i.e. excluding the contribution across the boundary in the plane z = 0 defined by 2 < x² + y < 5.
Let W be the three dimensional region under the graph of f(x, y) = exp[-2(x² + y)] and over the region in the plane z = 0 defined by 2 < x? + y < 5. (a) Use the divergence theorem to calculate the flux of F = (x y +2 x) i+ yj-yzk out of the region W. (b) Find the flux of F out of the part of the boundary of W for which z > 0, i.e. excluding the contribution across the boundary in the plane z = 0 defined by 2 < x² + y < 5.
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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![Let W be the three dimensional region under the graph of f(x, y) = exp[-2(x? + y?)] and over the region in the plane
z = 0 defined by 2 sx? + y? < 5.
(a) Use the divergence theorem to calculate the flux of F = (x y +2 x) i+ yj- yzk out of the region W.
(b) Find the flux of F out of the part of the boundary of W for which z > 0, i.e. excluding the contribution across the
boundary in the plane z = 0 defined by 2< x² + y < 5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39359a23-477e-4d56-b47f-f909907f6951%2F2d63f7d4-7e8c-4969-9631-dfa255a95b95%2F3ovtube_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let W be the three dimensional region under the graph of f(x, y) = exp[-2(x? + y?)] and over the region in the plane
z = 0 defined by 2 sx? + y? < 5.
(a) Use the divergence theorem to calculate the flux of F = (x y +2 x) i+ yj- yzk out of the region W.
(b) Find the flux of F out of the part of the boundary of W for which z > 0, i.e. excluding the contribution across the
boundary in the plane z = 0 defined by 2< x² + y < 5.
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