Let S = $(D), where D = {(u, v) : u² + v² ≤ 9,u ≥ 0, v ≥ 0} and Þ(u, v) = (2u + 1, u – v, 3u + v). (a) Calculate the surface area of S. (Express numbers in exact form. Use symbolic notation and fractions where needed.) area(S) = (b) Evaluate (4x – 4y) dS. Hint: Use polar coordinates. (Express numbers in exact form. Use symbolic notation and fractions where needed.) (4 (4x - 4y) ds = S

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let S = $(D), where D = {(u, v) : u² + v² ≤ 9,u ≥ 0, v ≥ 0} and Þ(u, v) = (2u + 1, u – v, 3u + v).
(a) Calculate the surface area of S.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
area(S) =
(b) Evaluate
(4x – 4y) dS.
Hint: Use polar coordinates.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
(4
(4x - 4y) ds =
S
Transcribed Image Text:Let S = $(D), where D = {(u, v) : u² + v² ≤ 9,u ≥ 0, v ≥ 0} and Þ(u, v) = (2u + 1, u – v, 3u + v). (a) Calculate the surface area of S. (Express numbers in exact form. Use symbolic notation and fractions where needed.) area(S) = (b) Evaluate (4x – 4y) dS. Hint: Use polar coordinates. (Express numbers in exact form. Use symbolic notation and fractions where needed.) (4 (4x - 4y) ds = S
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