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Exercise: 5 a) Find the outward flux of the vector field F(x, y, z) = x³i+y³j + (z³ + xz)k across the surface of the region that is enclosed by the hemisphere z = √√a²-x² - y² and the plane z = 0.

Exercise: 5 a) Find the outward flux of the vector field F(x, y, z) = x³i+y³j + (z³ + xz)k across the surface of the region that is enclosed by the hemisphere z = √√a²-x² - y² and the plane z = 0.

Advanced Engineering Mathematics
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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Exercise: 5 a) Find the outward flux of the vector field F(x, y, z) = x³i + y³j+ (z³ + xz)k across the surface of the region that is enclosed by the hemisphere z = a² – x² – y2 and the plane z = 0. b) Use the transformation u = 2x – y, v = x + 3y to find JJ, (2х-у)3 dA, where R is the rectangular region enclosed by the lines 2x – y = 0, 2x – y = 1, x + 3y = 1, x + 3y = 3.
Transcribed Image Text:Exercise: 5 a) Find the outward flux of the vector field F(x, y, z) = x³i + y³j+ (z³ + xz)k across the surface of the region that is enclosed by the hemisphere z = a² – x² – y2 and the plane z = 0. b) Use the transformation u = 2x – y, v = x + 3y to find JJ, (2х-у)3 dA, where R is the rectangular region enclosed by the lines 2x – y = 0, 2x – y = 1, x + 3y = 1, x + 3y = 3.
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