(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, 0sus 2, 0svs 2n. 27 O A(S) = V 4b?u* cos?(v) + 4a²uª sin²(v) + a²b?u² du dv r 27 (2bu? cos(v) + 2au² sin²(v) + abu) du dv O A(S) = r 2n O A(S) = V 4b?u* cos(v) + 4a²uª sin(v) + a²b?u² du dv O A(S) = || (2bu² + 2au? + abu) du dv O A(S) = V 4b?uª + 4a²uª + a²b?u² du dv
(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, 0sus 2, 0svs 2n. 27 O A(S) = V 4b?u* cos?(v) + 4a²uª sin²(v) + a²b?u² du dv r 27 (2bu? cos(v) + 2au² sin²(v) + abu) du dv O A(S) = r 2n O A(S) = V 4b?u* cos(v) + 4a²uª sin(v) + a²b?u² du dv O A(S) = || (2bu² + 2au? + abu) du dv O A(S) = V 4b?uª + 4a²uª + a²b?u² du dv
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 = u?, 0 <u< 2, 0< v < 2n.
O A(S) =
V 4b?u4 cos?(v) + 4a?u4 sin?(v) + a²b?u² du dv
2n
O A(S) =
(2bu? cos(v) + 2au? sin?(v) + abu) du dv
27
O A(S) =
T V4b?ut cos(v) + 4a²ut sin(v) + a?b?u? du dv
s (2bu? +
O A(S) =
2au?
+ abu) du dv
27
2
O A(S) =
V 4b?u4 + 4a²u4 + a?b?u² du dv
(b) For the case a = 2, b = 3, and for the constant vector field F(x,y,z) = 3i + k, find the flux of F through the surface S.
F-ds equals
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