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Let S be a smooth surface defined parametrically by r(u, v) = x(u, v)i + y(u, v where u and v are contained in a region R. Then the surface area of S is given by CC

Let S be a smooth surface defined parametrically by r(u, v) = x(u, v)i + y(u, v where u and v are contained in a region R. Then the surface area of S is given by CC

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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Set-up the double integral being asked, no need to evaluate. Show complete solutions and sketch the graph.

Definition: Area of a Parametric Surface Let S be a smooth surface defined parametrically by r(u, v) = x(u, v)i + y(u, v)ĵ + z(u, v)k where u and v are contained in a region IR. Then the surface area of S is given by = SS₁ || ru x roll R Let S be the surface defined by the vector function R(u, v) = (— — 2u, v + 5, ve“) SA= dudv. for all (u, v) € R². Set - up an iterated double integral, in terms of the parameters u and v, that gives the surface area of the portion of S whose projection on the xy - plane is the triangular region with vertices at the points (0,0), (0,5) and (1,5).
Transcribed Image Text:Definition: Area of a Parametric Surface Let S be a smooth surface defined parametrically by r(u, v) = x(u, v)i + y(u, v)ĵ + z(u, v)k where u and v are contained in a region IR. Then the surface area of S is given by = SS₁ || ru x roll R Let S be the surface defined by the vector function R(u, v) = (— — 2u, v + 5, ve“) SA= dudv. for all (u, v) € R². Set - up an iterated double integral, in terms of the parameters u and v, that gives the surface area of the portion of S whose projection on the xy - plane is the triangular region with vertices at the points (0,0), (0,5) and (1,5).
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