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Let S = Þ(D), where D = {(u, v) : u² + v² ≤ 1, 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) = √6 27 (b) Evaluate (3x − 3y) dS. Hint: Use polar coordinates.

Let S = Þ(D), where D = {(u, v) : u² + v² ≤ 1, 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) = √6 27 (b) Evaluate (3x − 3y) dS. Hint: Use polar coordinates.

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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Let S = Þ(D), where D = {(u, v) : u² + v² ≤ 1, 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) = Is √6 2 (b) Evaluate (3x – 3y) ds. Hint: Use polar coordinates. (Express numbers in exact form. Use symbolic notation and fractions where needed.) π Incorrect (3x - 3y) ds = √6 (8+3π) 12
Transcribed Image Text:Let S = Þ(D), where D = {(u, v) : u² + v² ≤ 1, 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) = Is √6 2 (b) Evaluate (3x – 3y) ds. Hint: Use polar coordinates. (Express numbers in exact form. Use symbolic notation and fractions where needed.) π Incorrect (3x - 3y) ds = √6 (8+3π) 12
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