Let S be the surface which is the graph of a C¹ function f(x, y) defined on an elementary region D. Then the area A(S) of S is given by f f //₁√ ₁ + 2√2 + 0/1/1 1 dx² dy² f(x, y) dxdy D af af °/₂√¹ + ( ) + ( ) 1 ² dy D dxdy of Vitrix, 1 + dxdy 1 - (3) ² (f)²³ dxdy axdy

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Let S be the surface which is the graph of a C¹ function f(x, y) defined on an elementary region D. Then the area A(S) of
S is given by
1/₂
1 +
. Fixy
D
f(x, y) dxdy
8 f
8 f
dx² dy²
D
+
af
° // √√¹ + ² + ( )³²
1
af
əx
dy
1
- (0)²
dxdy
dy
[/₂ √ ₁ + (f(x, y))³² dxdy
1
dxdy
dxdy
Transcribed Image Text:Let S be the surface which is the graph of a C¹ function f(x, y) defined on an elementary region D. Then the area A(S) of S is given by 1/₂ 1 + . Fixy D f(x, y) dxdy 8 f 8 f dx² dy² D + af ° // √√¹ + ² + ( )³² 1 af əx dy 1 - (0)² dxdy dy [/₂ √ ₁ + (f(x, y))³² dxdy 1 dxdy dxdy
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