(a) Set up, but do not evaluate, a double integral for the area of the surface S with parametric equations x = au cos(v), y = bu sin(v), z = u², o sus 2, 0suS 27. O A(S) = (2bu? cos(v) + 2au? sin2(v) + abu) du dv O A(S) = (2bu? + 2au? + abu) du dv O A(S) = V 4b?u4 + 4a²u4 + a?b?u² du dv 27 O A(S) = V 4b?u4 cos?(v) + 4a²u4 sin²(v) + a²b?u² du dv r27 O A(S) = V 4b?u“ cos(v) + 4a?u* sin(v) + a²b²u² du dv (b) For the case a = 3, b = 4, and for the constant vector field F(x,y,z) = 41+k, find the flux of F through the surface S. F•ds equals
(a) Set up, but do not evaluate, a double integral for the area of the surface S with parametric equations x = au cos(v), y = bu sin(v), z = u², o sus 2, 0suS 27. O A(S) = (2bu? cos(v) + 2au? sin2(v) + abu) du dv O A(S) = (2bu? + 2au? + abu) du dv O A(S) = V 4b?u4 + 4a²u4 + a?b?u² du dv 27 O A(S) = V 4b?u4 cos?(v) + 4a²u4 sin²(v) + a²b?u² du dv r27 O A(S) = V 4b?u“ cos(v) + 4a?u* sin(v) + a²b²u² du dv (b) For the case a = 3, b = 4, and for the constant vector field F(x,y,z) = 41+k, find the flux of F through the surface S. F•ds equals
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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Transcribed Image Text:(a) Set up, but do not evaluate, a double integral for the area of the surface S with parametric equations x = au cos(v), y = bu sin(v), z = u², osus 2, osv s 27.
O A(S) =
(2bu? cos(v) + 2au? sin2(v) + abu) du dv
27
O A(S) =
(2bu? + 2au? + abu) du dv
277
O A(S) =
V 4b?u4 + 4a²u4 + a²b?u² du dv
O A(S) =
V 4b?u4 cos?(v) + 4a?u4 sin?(v) + a²b?u² du dv
O A(S) =
V 4b?u4 cos(v) + 4a?u4 sin(v) + a²b?u² du dv
(b) For the case a = 3, b = 4, and for the constant vector field F(x,y,z) = 4 i + k, find the flux of F through the surface S.
F•ds equals
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